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

Author

Hugo Pfoertner, Sep 16 2011

Keywords

• nonn

Comments

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

Examples

			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.
		

References

• See A002091.

Links

• Hugo Pfoertner, Table of n, a(n) for n = 3..10000
• Wikipedia, Lemoine's conjecture

Crossrefs

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

Programs

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 *)