A167860 Primes p dividing every A167859(m) from m=(p-1)/2 to m=(p-1).

7, 47, 191, 383, 439, 1151, 1399, 2351, 2879, 3119, 3511, 3559, 4127, 5087, 5431, 6911, 8887, 9127, 9791, 9887, 12391, 13151, 14407, 15551, 16607, 19543, 20399, 21031, 21319, 21839, 23039, 25391, 26399, 28087, 28463, 28711, 29287, 33223, 39551, 43103, 44879, 46271

Offset

1,1

Comments

Apparently A167860 is a subset of primes of the form 8*k + 7 (A007522).

A167859(n) = 4^n*Sum_{ k=0..n } ((binomial(2*k,k))^2)/4^k.

Every A167859(m) from m=(p-1)/2 to m=(p-1) is divisible by prime p belonging to A167860.

7^3 divides A167859(13) and 7^2 divides A167859(10)-A167859(13).

Every A167859(m) from m=(kp-1 - (p-1)/2) to m=(kp-1) is divisible by prime p from A167860.

Every A167859(m) from m=((p^2-1)/2) to m=(p^2-1) is divisible by prime p from A167860. For p=7 every A167859(m) from m=((p^3-1)/2) to m=(p^3-1) and from m=((p^4-1)/2) to m(p^4-1)is divisible by p^2.

Links

Table of n, a(n) for n=1..42.

Prog

(PARI) is(p) = if(isprime(p)&&p%2, my(m=Mod(1, p), s=m); for(k=1, p\2, s+=(m*=(2*k-1)/k)^2); !s, 0); \\ Jinyuan Wang, Jul 24 2022

Crossrefs

Cf. A000984, A006134, A007522, A066796, A082590, A132310, A144635, A167713, A167859.

Sequence in context: A142185 A158914 A046872 * A152988 A336789 A201437

Adjacent sequences: A167857 A167858 A167859 * A167861 A167862 A167863

Keyword

nonn

Author

Alexander Adamchuk, Nov 13 2009

Extensions

More terms from Jinyuan Wang, Jul 24 2022

Status

approved