A298763 - OEIS

%I #20 Sep 03 2020 15:09:40

%S 19,29,1303,3119,4933,6353,7841,10859,13933,24749,26513,28603,31069,

%T 33487,38609,43067,52387,53731,61979,78031,91781,93871,97561,102929,

%U 108127,112403,113341,114599,141937,144967,151883,151969,192883,224909,267961,270371,270577,270763,281531,282959,285979

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

%H Hans Havermann, <a href="/A298763/b298763.txt">Table of n, a(n) for n = 1..10000</a>

%e 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.

%t 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}]]

%Y Subsequence of A073681.

%K nonn

%O 1,1

%A _Hans Havermann_, Jan 26 2018