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A341326 Primes p such that p+j, p+k, q+j, q+k are all prime, where q is the next prime after p, j = p mod A007953(q) and k = q mod A007953(p). 1

%I #13 Feb 09 2021 21:40:43

%S 28643,36749,77687,207497,375091,507137,510061,597419,652543,810343,

%T 869413,910201,967397,1021283,1219831,1246879,1653101,1673741,1830331,

%U 1944311,2386271,2415449,2604731,3135023,3288529,3622721,3714031,4227031,4812413,6208591,7250197,7308241,7337683,7447061,7451981,7513577

%N Primes p such that p+j, p+k, q+j, q+k are all prime, where q is the next prime after p, j = p mod A007953(q) and k = q mod A007953(p).

%H Robert Israel, <a href="/A341326/b341326.txt">Table of n, a(n) for n = 1..2500</a>

%e a(3) = 77687 is a term because with p = 77687, q = 77689, k = p mod 37 = 24, j = q mod 35 = 24, and p+j = p+k = 77711 and q+j = q+k = 77713 are prime.

%p filter:= proc(p,q) local k,j;

%p k:= p mod convert(convert(q,base,10),`+`);

%p j:= q mod convert(convert(p,base,10),`+`);

%p andmap(isprime,{p+k,q+k,p+j,q+j});

%p end proc:

%p q:= 2:

%p count:= 0: R:= NULL:

%p while q < 10^7 do

%p p:= q; q:= nextprime(q);

%p if filter(p,q) then count:= count+1; R:= R,p; fi

%p od:

%Y Cf. A007953.

%K nonn,base

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Feb 09 2021

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Last modified March 28 22:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)