47563

Properties

Appears in sequences

• Let p_n be the polynomial of degree n-1 that interpolates the first n primes (i.e., p_n(i) = prime(i) for 1 <= i <= n.) Then a(n) = p_n(n+1)/2.at n=17A121049
• Primes p such that continued fraction of (1 + sqrt(p))/2 has period 10 : primes in A146335.at n=21A146355
• Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, 1), (-1, 0, 1), (-1, 1, -1), (-1, 1, 0), (1, 0, 0)}.at n=11A148532
• Primes formed by rearranging five consecutive decimal digits (avoiding leading 0).at n=24A156119
• Maximum water retention of a number square of order n.at n=18A261347
• Let u defined by u(1) = p and for 1 < i, u(i) = u(i-1) + primorial(i), such that all u(i) are primes for 1 <= i <= k, and u(k+1) is not prime. Let m the length of the longest run of primes obtained when u is repeatedly applied to an n-digit p. Triangle read by rows: for 1 <= n, 1 <= k <= m, T(n,k) is the least n-digit prime p beginning a run of only k primes when applied u, or -1 if no such prime p exists.at n=40A356732
• Prime numbersat n=4903