A112545 Least odd number k greater than 1 such that the sum of the predecessor and successor primes of the n-th prime is divisible by k or if no such odd k exists then 2.

7, 5, 2, 5, 7, 2, 5, 3, 3, 3, 3, 5, 11, 3, 53, 3, 3, 3, 5, 3, 3, 3, 3, 5, 5, 13, 53, 5, 59, 61, 3, 3, 11, 5, 3, 157, 3, 3, 173, 3, 5, 11, 97, 7, 3, 211, 3, 113, 5, 3, 3, 5, 3, 257, 263, 3, 3, 3, 5, 7, 5, 151, 5, 157, 7, 3, 3, 7, 5, 3, 3, 3, 373, 3, 3, 3, 5, 13, 5, 5, 5, 7, 3, 3, 3, 3, 5, 5, 29, 3, 3

Offset

2,1

Comments

From Robert Israel, Apr 20 2017: (Start)

a(n) = A078701(prime(n-1)+prime(n+1)) unless that is 1, in which case a(n)=2.

a(n) = 2 if and only if for some m, A007053(m) = n or n-1 with prime(n-1)+prime(n+1) = 2^(m+1). The first m for which this occurs are 3,4,9,379,593, corresponding to n = 4,7,97 and approximately 3*10^116 and 1*10^181. Are there infinitely many? (End)

Links

Robert Israel, Table of n, a(n) for n = 2..10000

Maple

f:= proc(n) local t; t:= min(numtheory:-factorset(ithprime(n-1)+ithprime(n+1)) minus {2}); if t::integer then t else 2 fi end proc:
map(f, [$2..200]); # Robert Israel, Apr 20 2017

Mathematica

f[n_] := Block[{k = 3, s = Prime[n - 1] + Prime[n + 1]}, While[Mod[s, k] != 0 && k <= s, k += 2]; If[k > s, 2, k]]; Table[ f[n], {n, 2, 92}]

Prog

(PARI) a(n) = {p = prime(n); s = precprime(p-1) + nextprime(p+1); f = factor(s); if (#f~ > 1, f[2, 1], f[1, 1]); } \\ Michel Marcus, Apr 22 2017

Crossrefs

Cf. A000040, A112686, A112681, A112794, A112731, A112789, A112795, A112796, A112804, A112847, A112859, A113155, A113156, A113157, A113158.

Cf. A007053, A078701.

Sequence in context: A135537 A212038 A335863 * A021934 A021097 A307160

Adjacent sequences: A112542 A112543 A112544 * A112546 A112547 A112548

Keyword

nonn

Author

Robert G. Wilson v, Jan 11 2006

Status

approved