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A118860 Numbers k such that k-1, k+1, 2k-1, 2k+1, 3k-1, 3k+1, 4k-1 and 4k+1 are all primes.

%I A118860 #36 Mar 13 2025 05:09:23
%S A118860 21968100,37674210,81875220,356467230,416172330,750662640,1007393730,
%T A118860 1150070040,1586271960,1963954650,3127171320,3669568560,4377895410,
%U A118860 4383541050,5575083360,5686935870,5708418870,7365234450,7478474430,7681046100,8453862690,8898688680
%N A118860 Numbers k such that k-1, k+1, 2k-1, 2k+1, 3k-1, 3k+1, 4k-1 and 4k+1 are all primes.
%C A118860 All terms are multiples of 210, hence simpler code is possible.
%H A118860 Amiram Eldar, <a href="/A118860/b118860.txt">Table of n, a(n) for n = 1..100</a>
%F A118860 a(n) = 210*A174293(n).
%e A118860 21968100 is a term because 21968099, 21968101, 43936199, 43936201, 65904299, 65904301, 87872399, 87872401 are all prime.
%t A118860 tb={};Do[If[(PrimeQ[n-1]&&PrimeQ[n+1])&& (PrimeQ[2*n-1]&&PrimeQ[2*n+1])&& (PrimeQ[3*n-1]&&PrimeQ[3*n+1])&& (PrimeQ[4*n-1]&&PrimeQ[4*n+1]), Print[n];AppendTo[tb,n]], {n,21968100,10^8,210}];tb
%t A118860 Select[210*Range[424*10^5],AllTrue[{#-1,#+1,2#-1,2#+1,3#-1,3#+1,4#-1,4#+1},PrimeQ]&] (* _Harvey P. Dale_, Jul 23 2024 *)
%o A118860 (PARI) isok(k) = if(k % 210, 0, for(i = 1, 4, forstep(j = -1, 1, 2, if(!isprime(i*k-j), return(0)))); 1); \\ _Amiram Eldar_, Mar 13 2025
%Y A118860 Subsequence of A014574, A066388 and A118859.
%Y A118860 Subsequence: A349321.
%Y A118860 Cf. A174293, A348348.
%K A118860 nonn
%O A118860 1,1
%A A118860 _Labos Elemer_, May 03 2006
%E A118860 Edited by _Don Reble_, May 16 2006
%E A118860 a(20)-a(22) from _Pontus von Brömssen_, Oct 14 2021