A195352 Smallest prime p such that 2*n+1 = 2*p + q for some odd prime q.

2, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 3, 7, 2, 2, 3, 5, 2, 3, 2, 2, 3, 2, 3, 7, 2, 3, 7, 2, 2, 3, 5, 2, 3, 2, 2, 3, 5, 2, 3, 2, 3, 19, 2, 3, 7, 5, 2, 3, 2, 2, 3, 2, 2, 3, 2, 3, 7, 5, 11, 7, 11, 2, 3, 2, 3, 13, 2, 2, 3, 5, 5, 7, 2, 2, 3, 5, 2, 3, 7, 2, 3, 2, 3, 13

Offset

3,1

Comments

Related to Lemoine's conjecture, which states that all odd integers > 5 can be represented as 2*p+q, p, q primes.

References

See A002091.

Links

Hugo Pfoertner, Table of n, a(n) for n = 3..10000

Wikipedia, Lemoine's conjecture

Example

a(3)=2 because 2*3+1=7=2*2+3; a(4)=2: 2*3+1=9=2*2+5; a(5)=2: 11=2*2+7; a(6)=3: 13=2*3+7.

Mathematica

spp[n_]:=Module[{p=2}, While[CompositeQ[(2n+1)-2p], p=NextPrime[p]]; p]; Array[ spp, 90, 3] (* Harvey P. Dale, Jun 02 2022 *)

Crossrefs

Cf. A002091, A103506 (smallest q), A046927, A195353 (positions of records), A195354 (records), A103153 (prime p=2 excluded), A185091.

Sequence in context: A173883 A022922 A239141 * A103507 A219252 A290839

Adjacent sequences: A195349 A195350 A195351 * A195353 A195354 A195355

Keyword

nonn

Author

Hugo Pfoertner, Sep 16 2011

Status

approved