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Strongly-single primes: primes p such that neither previousprime(p) nor nextprime(p) is a twin prime.
2

%I #17 Sep 08 2022 08:45:30

%S 83,89,127,163,167,257,331,359,367,373,379,383,389,397,401,443,449,

%T 479,487,491,499,503,547,557,587,677,683,691,701,709,719,727,733,739,

%U 743,751,757,761,769,773,787,907,911,919,929,937,941,947,953,967,971,977

%N Strongly-single primes: primes p such that neither previousprime(p) nor nextprime(p) is a twin prime.

%H Amiram Eldar, <a href="/A130286/b130286.txt">Table of n, a(n) for n = 1..10000</a>

%t PrimeNext[n_]:=Module[{k},k=n+1;While[ !PrimeQ[k],k++ ];k]; PrimePrev[n_]:=Module[{k},k=n-1;While[ !PrimeQ[k],k-- ];k]; lst={};Do[p=Prime[n];If[ !PrimeQ[p-2]&&!PrimeQ[PrimePrev[p]-2]&&!PrimeQ[p+2]&&!PrimeQ[PrimeNext[p]+2],AppendTo[lst,p]],{n,6!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Jul 21 2009 *)

%o (Magma) f:=func<p|NextPrime(p)>; g:=func<p|PreviousPrime(p)>; [p: p in PrimesInInterval(5,1000)| not IsPrime(f(p)-2) and not IsPrime(g(p)+2) and not IsPrime(f(f(p))-2) and not IsPrime(g(g(p))+2)]; // _Marius A. Burtea_, Jan 02 2020

%Y Cf. A000040 (primes), A001097 (twin primes), A007510 (single primes), A071904 (odd composite numbers).

%K nonn

%O 1,1

%A _Zak Seidov_, Aug 06 2007

%E Some terms corrected by _Vladimir Joseph Stephan Orlovsky_, Jul 21 2009