A112686 -id:A112686 - cp's OEIS frontend

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

Robert G. Wilson v, Jan 11 2006

nonn

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)

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

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

Cf. A007053, A078701.

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

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}]

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

cp's OEIS Frontend

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.

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