A121764 - OEIS

%I #48 Sep 08 2022 08:45:27

%S 37,67,79,97,127,157,163,211,223,277,307,331,337,367,373,379,397,409,

%T 439,457,487,499,541,547,577,607,613,631,673,691,709,727,733,739,751,

%U 757,769,787,853,877,907,919,937,967,991,997,1009,1039,1069,1087,1117

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

%C 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

%C Subsequence of A002476. - _Michel Marcus_, Apr 26 2015

%H Zak Seidov, <a href="/A121764/b121764.txt">Table of n, a(n) for n = 1..10000</a>

%H Zak Seidov, <a href="/A121764/a121764.jpg">Plot of A121764(n) - A121762(n)</a>

%t Select[Table[6n + 1, {n, 200}], PrimeQ[#] && !PrimeQ[#-2] &] (* _Ray Chandler_, Aug 22 2006 *)

%t Select[Prime[Range[200]],Mod[#,6]==1&&NoneTrue[#+{2,-2},PrimeQ]&] (* _Harvey P. Dale_, Jul 16 2021 *)

%o (PARI) {is(n)=n%6==1 && isprime(n) && !isprime(n-2)}; \\ _G. C. Greubel_, Feb 26 2019

%o (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

%o (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

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

%K nonn

%O 1,1

%A _Lekraj Beedassy_, Aug 20 2006

%E Extended by _Ray Chandler_, Aug 22 2006