A163488 Primes p such that 5*p is a sum of 3 consecutive primes.

2, 3, 47, 79, 113, 197, 227, 257, 263, 317, 347, 383, 431, 443, 491, 499, 541, 557, 617, 757, 811, 887, 929, 977, 1021, 1087, 1093, 1129, 1231, 1237, 1433, 1511, 2111, 2129, 2213, 2347, 2543, 2551, 2609, 2657, 2671, 2803, 2837, 2999, 3011, 3049, 3119, 3187

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jul 28 2009

Keywords

• nonn

Comments

Primes of the form A034961(k)/5, associated with k=1, 2, 21, 31, 42, 66,... - R. J. Mathar, Aug 02 2009

Examples

			p=2 is in the sequence because 2*5=10=2+3+5.
p=3 is in the sequence because 3*5=15=3+5+7.
		

Crossrefs

Cf. A006562, A118134, A163487.

Programs

Mathematica

lst={};Do[If[PrimeQ[p=(Prime[n]+Prime[n+1]+Prime[n+2])/5],AppendTo[lst, p]],{n,7!}];lst
cp3Q[n_]:=Module[{mid=Floor[PrimePi[(5n)/3]],tst},tst=Total/@ Partition[ Prime[ Range[mid-10,mid+10]],3,1];MemberQ[tst,5n]]; Select[ Prime[ Range[ 500]],cp3Q]//Quiet (* Harvey P. Dale, Jan 02 2018 *)

Extensions

Entries checked by R. J. Mathar, Aug 02 2009