Sequences

392,541 sequences

Duplicate of A026137.A026211
Duplicate of A026137.
Duplicate of A026188.A026212
Duplicate of A026188.
Duplicate of A026189.A026213
Duplicate of A026189.
a(n) = (1/2)*s(n), where s(n) is the n-th even number in A026177.A026214
a(n) = (1/2)*s(n), where s(n) is the n-th even number in A026177.
a(n) is the position of n in A026214.A026215
a(n) is the position of n in A026214.
Duplicate of A026177.A026216
Duplicate of A026177.
Duplicate of A026178.A026217
Duplicate of A026178.
a(n) = (1/3)*(s(n) + 2), where s(n) is the n-th number congruent to 1 mod 3 in A026177.A026218
a(n) = (1/3)*(s(n) + 2), where s(n) is the n-th number congruent to 1 mod 3 in A026177.
Position of n in A026218.A026219
Position of n in A026218.
Duplicate of A026215.A026220
Duplicate of A026215.
Duplicate of A026214.A026221
Duplicate of A026214.
Numbers k such that A026136(k) = A026142(k).A026222
Numbers k such that A026136(k) = A026142(k).
(1/3)*s(n+1), where s = A026222.A026223
(1/3)*s(n+1), where s = A026222.
Numbers n such that t(n) = s(n) + 1, where s = A026136, t = A026142.A026224
Numbers n such that t(n) = s(n) + 1, where s = A026136, t = A026142.
Numbers of the form 3^i * (3k+1).A026225
Numbers of the form 3^i * (3k+1).
Numbers k such that A026136(k) = A026166(k).A026226
Numbers k such that A026136(k) = A026166(k).
a(n) = (1/3)*(s(n) + 2), where s = A026226.A026227
a(n) = (1/3)*(s(n) + 2), where s = A026226.
Numbers k such that A026166(k) = A026136(k) - 1.A026228
Numbers k such that A026166(k) = A026136(k) - 1.
Numbers k such that A026166(k) = A026142(k) - 2.A026229
Numbers k such that A026166(k) = A026142(k) - 2.
a(n) = (1/3)*s(n+1), where s = A026229.A026230
a(n) = (1/3)*s(n+1), where s = A026229.
Numbers k such that A026166(k) = A026142(k) + 1.A026231
Numbers k such that A026166(k) = A026142(k) + 1.
a(n) = (1/3)*(s(n) + 1), where s = A026231.A026232
a(n) = (1/3)*(s(n) + 1), where s = A026231.
a(n) = j if n is the j-th prime, else a(n) = k if n is the k-th nonprime.A026233
a(n) = j if n is the j-th prime, else a(n) = k if n is the k-th nonprime.
In the sequence of positive integers, swap the k-th prime and k-th nonprime, for k = 1,2,3,...A026234
In the sequence of positive integers, swap the k-th prime and k-th nonprime, for k = 1,2,3,...
a(n) = |s(n) - n|, where s = A026234.A026235
a(n) = |s(n) - n|, where s = A026234.
a(n) = (s(n) + 1)/2, where s(n) is the n-th odd number in A026234.A026236
a(n) = (s(n) + 1)/2, where s(n) is the n-th odd number in A026234.
a(n) = position of n in A026236.A026237
a(n) = position of n in A026236.
a(n) = j if n is the j-th prime, else a(n) = k if n is the k-th composite.A026238
a(n) = j if n is the j-th prime, else a(n) = k if n is the k-th composite.
Beginning with the natural numbers, swap the k-th prime and k-th composite.A026239
Beginning with the natural numbers, swap the k-th prime and k-th composite.
a(n) = |s(n) - n|, where s = A026239.A026240
a(n) = |s(n) - n|, where s = A026239.
Expansion of 1/((1-2*x)*(1-5*x)*(1-10*x)*(1-12*x)).A026241
Expansion of 1/((1-2*x)*(1-5*x)*(1-10*x)*(1-12*x)).
a(n) = j if n is L(j), else a(n) = k if n is U(k), where L = A000201, U = A001950 (lower and upper Wythoff sequences).A026242
a(n) = j if n is L(j), else a(n) = k if n is U(k), where L = A000201, U = A001950 (lower and upper Wythoff sequences).
a(n) = A000522(n) - 2.A026243
a(n) = A000522(n) - 2.
a(n) = 4^n*(4^n+1)/2.A026244
a(n) = 4^n*(4^n+1)/2.
a(n) = (1/2)*(s(n) + 1), where s(n) is the n-th odd number in A002251.A026245
a(n) = (1/2)*(s(n) + 1), where s(n) is the n-th odd number in A002251.
position of n in A026245.A026246
position of n in A026245.
a(n) = (1/2)*s(n), where s(n) is n-th even number in A002251.A026247
a(n) = (1/2)*s(n), where s(n) is n-th even number in A002251.
a(n) = position of n in A026247.A026248
a(n) = position of n in A026247.
a(n) = j if n = [ j*sqrt(2) ], else a(n) = k if n = [ k*(2 + sqrt(2)) ].A026249
a(n) = j if n = [ j*sqrt(2) ], else a(n) = k if n = [ k*(2 + sqrt(2)) ].
Beginning with the natural numbers, swap [ k*sqrt(2) ] and [ k*(2 + sqrt(2)) ], for all k >= 1.A026250
Beginning with the natural numbers, swap [ k*sqrt(2) ] and [ k*(2 + sqrt(2)) ], for all k >= 1.
a(n) = |s(n) - n|, where s = A026250. Also a(n) = 2*t(n), where t = A026249.A026251
a(n) = |s(n) - n|, where s = A026250. Also a(n) = 2*t(n), where t = A026249.
a(n) = (1/2)*(s(n) + 1), where s(n) is the n-th odd number in A026250. Also a(n) = position of n in A026252.A026252
a(n) = (1/2)*(s(n) + 1), where s(n) is the n-th odd number in A026250. Also a(n) = position of n in A026252.
a(n) = (1/2)*s(n), where s(n) is the n-th even number in A026250. Also a(n) = position of n in A026253.A026253
a(n) = (1/2)*s(n), where s(n) is the n-th even number in A026250. Also a(n) = position of n in A026253.
a(n) = j if n = [ j*sqrt(3) ], else a(n) = k if n = [ (k/2)*(3 + sqrt(3)) ].A026254
a(n) = j if n = [ j*sqrt(3) ], else a(n) = k if n = [ (k/2)*(3 + sqrt(3)) ].
Beginning with the natural numbers, swap [ k*sqrt(3) ] and [ (k/2)*(3 + sqrt(3)) ], for all k >= 1.A026255
Beginning with the natural numbers, swap [ k*sqrt(3) ] and [ (k/2)*(3 + sqrt(3)) ], for all k >= 1.
a(n) = |s(n) - n|, where s = A026255.A026256
a(n) = |s(n) - n|, where s = A026255.
a(n) = (1/2)*(s(n) + 1), where s(n) is the n-th odd number in A026255.A026257
a(n) = (1/2)*(s(n) + 1), where s(n) is the n-th odd number in A026255.
Position of n in A026257.A026258
Position of n in A026257.
a(n) = (1/2)*s(n), where s(n) is the n-th even number in A026255.A026259
a(n) = (1/2)*s(n), where s(n) is the n-th even number in A026255.
Position of n in A026259.A026260
Position of n in A026259.