A121764 Single (or isolated or non-twin) primes of form 6n + 1.

37, 67, 79, 97, 127, 157, 163, 211, 223, 277, 307, 331, 337, 367, 373, 379, 397, 409, 439, 457, 487, 499, 541, 547, 577, 607, 613, 631, 673, 691, 709, 727, 733, 739, 751, 757, 769, 787, 853, 877, 907, 919, 937, 967, 991, 997, 1009, 1039, 1069, 1087, 1117

Offset: 1

Author

Lekraj Beedassy, Aug 20 2006

Keywords

• nonn

Comments

For the first 30000 terms a(n) > A121762(n), see plot A121764(n) - A121762(n). But is it so for all n? - Zak Seidov, Apr 25 2015

Subsequence of A002476. - Michel Marcus, Apr 26 2015

Links

• Zak Seidov, Table of n, a(n) for n = 1..10000
• Zak Seidov, Plot of A121764(n) - A121762(n)

Crossrefs

Cf. A007510, A121765, A002476, A121762, A038179, A007310, A038511.

Programs

Magma

[n: n in [1..1150] | (n mod 6 eq 1) and not IsPrime(n-2) and  IsPrime(n)]; // G. C. Greubel, Feb 26 2019

Mathematica

Select[Table[6n + 1, {n, 200}], PrimeQ[#] && !PrimeQ[#-2] &] (* Ray Chandler, Aug 22 2006 *)
Select[Prime[Range[200]],Mod[#,6]==1&&NoneTrue[#+{2,-2},PrimeQ]&] (* Harvey P. Dale, Jul 16 2021 *)

PARI

{is(n)=n%6==1 && isprime(n) && !isprime(n-2)}; \\ G. C. Greubel, Feb 26 2019

Sage

[n for n in (1..1150) if mod(n,6)==1 and not is_prime(n-2) and is_prime(n)] # G. C. Greubel, Feb 26 2019

Extensions

Extended by Ray Chandler, Aug 22 2006