A053072 - OEIS

%I #29 Dec 08 2024 14:57:05

%S 211,1511,4409,4691,7841,9871,11299,11411,11731,12841,15161,16619,

%T 17431,17851,18341,18731,19739,19949,20161,20521,20731,21661,22051,

%U 22259,23801,25621,26041,28069,29599,30059,31051,32479,34171,35129

%N Primes p such that p-12, p and p+12 are consecutive primes.

%C In other words, balanced primes separated from the next lower and next higher prime neighbors by 12.

%D J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 211, p. 61, Ellipses, Paris, 2008.

%H Zak Seidov, <a href="/A053072/b053072.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A052188(n) + 12. - _Michel Marcus_, Jan 09 2015

%e 1511 is separated from both the next lower prime and the next higher prime by 12.

%p for i from 1 by 1 to 5000 do if ithprime(i+1) = ithprime(i) +12 and ithprime(i+2) = ithprime(i) + 24 then print(ithprime(i+1)); # _Zerinvary Lajos_, May 04 2007

%t lst={};Do[p=Prime[n];If[p-Prime[n-1]==Prime[n+1]-p==6*2,AppendTo[lst,p]],{n,2,2*7!}];lst (* _Vladimir Joseph Stephan Orlovsky_, May 20 2010 *)

%t Transpose[Select[Partition[Prime[Range[4000]],3,1],Differences[#] == {12,12}&]][[2]] (* _Harvey P. Dale_, Apr 07 2013 *)

%Y Cf. A052188.

%K easy,nonn

%O 1,1

%A _Harvey P. Dale_, Feb 25 2000

%E Corrected by _Jud McCranie_, Jan 04 2001

%E Edited by _N. J. A. Sloane_, Jul 03 2008 at the suggestion of _R. J. Mathar_