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Least of 4 consecutive integers such that their product +-5 are primes.
2

%I #11 Jun 09 2023 22:19:02

%S 1,11,31,61,116,131,321,336,906,1081,1101,1216,1601,1821,2081,2106,

%T 2356,2491,3051,3101,3281,3286,3496,3736,4576,4716,4861,4876,4886,

%U 4981,5066,5096,5301,5881,6066,6121,6401,6761,6916,7061,7446,7556,8021,8041,8056

%N Least of 4 consecutive integers such that their product +-5 are primes.

%C 1*2*3*4=24+-5 -> primes,..

%H Harvey P. Dale, <a href="/A174244/b174244.txt">Table of n, a(n) for n = 1..1000</a>

%t f1[n_]:=PrimeQ[n-5]&&PrimeQ[n+5];f2[n_]:=n*(n+1)*(n+2)*(n+3);lst={};Do[If[f1[f2[n]],AppendTo[lst,n]],{n,8!}];lst

%t Select[Partition[Range[8200],4,1],AllTrue[Times@@#+{5,-5},PrimeQ]&][[All, 1]] (* or *) Select[ Range[ 8200],AllTrue[6#+11#^2+6#^3+#^4+{5,-5},PrimeQ]&] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Jun 20 2021 *)

%Y Cf. A014574, A174242, A174243.

%K nonn

%O 1,2

%A _Vladimir Joseph Stephan Orlovsky_, Mar 13 2010