Sequences

392,541 sequences

"Magic" integers: a(n+1) is the smallest integer m such that there is no overlap between the sets {m, m-a(i), m+a(i): 1 <= i <= n} and {a(i), a(i)-a(j), a(i)+a(j): 1 <= j < i <= n}.A004210
"Magic" integers: a(n+1) is the smallest integer m such that there is no overlap between the sets {m, m-a(i), m+a(i): 1 <= i <= n} and {a(i), a(i)-a(j), a(i)+a(j): 1 <= j < i <= n}.
Shifts one place left under 2nd-order binomial transform.A004211
Shifts one place left under 2nd-order binomial transform.
Shifts one place left under 3rd-order binomial transform.A004212
Shifts one place left under 3rd-order binomial transform.
Shifts one place left under 4th-order binomial transform.A004213
Shifts one place left under 4th-order binomial transform.
Positive numbers that are not the sum of three nonzero squares.A004214
Positive numbers that are not the sum of three nonzero squares.
Numbers that are the sum of 4 but no fewer nonzero squares.A004215
Numbers that are the sum of 4 but no fewer nonzero squares.
a(n) = floor(log_10(n)).A004216
a(n) = floor(log_10(n)).
a(n) = (n^n)^(n^n).A004217
a(n) = (n^n)^(n^n).
a(n) = log_10(n) rounded up.A004218
a(n) = log_10(n) rounded up.
a(n) = floor(10*log_10(n)).A004219
a(n) = floor(10*log_10(n)).
a(n) = 10*log_10(n) rounded to the nearest integer.A004220
a(n) = 10*log_10(n) rounded to the nearest integer.
a(n) = ceiling(10*log_10(n)).A004221
a(n) = ceiling(10*log_10(n)).
a(n) = 100*log_10(n) rounded down.A004222
a(n) = 100*log_10(n) rounded down.
a(n) = 100*log_10(n) rounded to the nearest integer.A004223
a(n) = 100*log_10(n) rounded to the nearest integer.
a(n) = 100*log_10(n) rounded up.A004224
a(n) = 100*log_10(n) rounded up.
a(n) = 1000*log_10(n) rounded down.A004225
a(n) = 1000*log_10(n) rounded down.
a(n) = 1000*log_10(n) rounded to the nearest integer.A004226
a(n) = 1000*log_10(n) rounded to the nearest integer.
a(n) = ceiling(1000*log_10(n)).A004227
a(n) = ceiling(1000*log_10(n)).
a(n) = 10000*log_10(n) rounded down.A004228
a(n) = 10000*log_10(n) rounded down.
a(n) = 10000*log_10(n) rounded to the nearest integer.A004229
a(n) = 10000*log_10(n) rounded to the nearest integer.
a(n) = 10000*log_10(n) rounded up.A004230
a(n) = 10000*log_10(n) rounded up.
Ackermann's sequence: n^^n := n^n^n^...^n (with n n's).A004231
Ackermann's sequence: n^^n := n^n^n^...^n (with n n's).
a(n) = n^2 + prime(n).A004232
a(n) = n^2 + prime(n).
a(n) = ceiling(log(n)).A004233
a(n) = ceiling(log(n)).
a(n) = floor(10*log(n)).A004234
a(n) = floor(10*log(n)).
a(n) = 10*log(n) rounded to the nearest integer.A004235
a(n) = 10*log(n) rounded to the nearest integer.
a(n) = ceiling(10*log(n)).A004236
a(n) = ceiling(10*log(n)).
a(n) = floor(100*log(n)).A004237
a(n) = floor(100*log(n)).
a(n) = 100*log(n) rounded to nearest integer.A004238
a(n) = 100*log(n) rounded to nearest integer.
a(n) = ceiling(100*log(n)).A004239
a(n) = ceiling(100*log(n)).
a(n) = floor(1000*log(n)).A004240
a(n) = floor(1000*log(n)).
a(n) = 1000*log(n) rounded to the nearest integer.A004241
a(n) = 1000*log(n) rounded to the nearest integer.
a(n) = ceiling(1000*log(n)).A004242
a(n) = ceiling(1000*log(n)).
a(n) = floor(10000*log(n)).A004243
a(n) = floor(10000*log(n)).
a(n) = 10000*log(n) rounded to nearest integer.A004244
a(n) = 10000*log(n) rounded to nearest integer.
a(n) = ceiling(10000*log(n)).A004245
a(n) = ceiling(10000*log(n)).
Number of permutations of length n with spread 3.A004246
Number of permutations of length n with spread 3.
Multiplication table read by antidiagonals: T(i,j) = i*j (i>=0, j>=0). Alternatively, multiplication triangle read by rows: P(i,j) = j*(i-j) (i>=0, 0<=j<=i).A004247
Multiplication table read by antidiagonals: T(i,j) = i*j (i>=0, j>=0). Alternatively, multiplication triangle read by rows: P(i,j) = j*(i-j) (i>=0, 0<=j<=i).
Array read by ascending antidiagonals: A(n, k) = k^n.A004248
Array read by ascending antidiagonals: A(n, k) = k^n.
a(n) = (2^2^...^2) (with n 2's) + 1.A004249
a(n) = (2^2^...^2) (with n 2's) + 1.
Number of partitions of n into 3 or more parts.A004250
Number of partitions of n into 3 or more parts.
Number of graphical partitions (degree-vectors for simple graphs with n vertices, or possible ordered row-sum vectors for a symmetric 0-1 matrix with diagonal values 0).A004251
Number of graphical partitions (degree-vectors for simple graphs with n vertices, or possible ordered row-sum vectors for a symmetric 0-1 matrix with diagonal values 0).
Path sums of n-point graphs.A004252
Path sums of n-point graphs.
a(n) = 5*a(n-1) - a(n-2), with a(1)=1, a(2)=4.A004253
a(n) = 5*a(n-1) - a(n-2), with a(1)=1, a(2)=4.
a(n) = 5*a(n-1) - a(n-2) for n > 1, a(0) = 0, a(1) = 1.A004254
a(n) = 5*a(n-1) - a(n-2) for n > 1, a(0) = 0, a(1) = 1.
a(n) = n*(n + 1)*(n^2 - 3*n + 6)/8.A004255
a(n) = n*(n + 1)*(n^2 - 3*n + 6)/8.
a(n) = n^2*(n+1)*(n+2)^2/6.A004256
a(n) = n^2*(n+1)*(n+2)^2/6.
a(n) = round(log_2(n)).A004257
a(n) = round(log_2(n)).
Duplicate of A029837.A004258
Duplicate of A029837.
a(n) = floor(10*log_2(n)).A004259
a(n) = floor(10*log_2(n)).