A130286 Strongly-single primes: primes p such that neither previousprime(p) nor nextprime(p) is a twin prime.

83, 89, 127, 163, 167, 257, 331, 359, 367, 373, 379, 383, 389, 397, 401, 443, 449, 479, 487, 491, 499, 503, 547, 557, 587, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Mathematica

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A031961 A108751 A256520 * A372042 A226380 A062677

Adjacent sequences: A130283 A130284 A130285 * A130287 A130288 A130289

Keyword

nonn

Author

Zak Seidov, Aug 06 2007

Extensions

Some terms corrected by Vladimir Joseph Stephan Orlovsky, Jul 21 2009

Status

approved