A298763 Numbers that are the smallest of four consecutive primes, no three of which sum to a nonprime.

19, 29, 1303, 3119, 4933, 6353, 7841, 10859, 13933, 24749, 26513, 28603, 31069, 33487, 38609, 43067, 52387, 53731, 61979, 78031, 91781, 93871, 97561, 102929, 108127, 112403, 113341, 114599, 141937, 144967, 151883, 151969, 192883, 224909, 267961, 270371, 270577, 270763, 281531, 282959, 285979

Offset: 1

Author

Hans Havermann, Jan 26 2018

Keywords

• nonn

Examples

			19, 23, 29, 31 are four consecutive primes. The four ways of adding three of them yields 71, 73, 79, 83, all of which are prime. So 19 is a term of the sequence.
		

Links

• Hans Havermann, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A073681.

Programs

Mathematica

s={2,3,5,7}; p=s[[-1]]; While[p<10^6, If[PrimeQ[s[[1]]+s[[2]]+s[[3]]]&&PrimeQ[s[[1]]+s[[2]]+s[[4]]]&&PrimeQ[s[[1]]+s[[3]]+s[[4]]]&&PrimeQ[s[[2]]+s[[3]]+s[[4]]], Print[s[[1]]]]; p=NextPrime[p]; s=Join[Rest[s],{p}]]