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Primes p such that the differences between the 5 consecutive primes starting with p are (4,6,6,2).
2

%I #25 Oct 20 2023 15:54:03

%S 43,163,643,1213,2953,4003,7573,11923,14533,25453,26683,26713,29863,

%T 41593,48523,61543,68473,150193,151153,172423,206803,227593,290023,

%U 302563,338563,343813,346543,428023,527053,529033,540373,547483,551713

%N Primes p such that the differences between the 5 consecutive primes starting with p are (4,6,6,2).

%C Equivalently, p, p+4, p+10, p+16 and p+18 are consecutive primes.

%C Subsequence of A078852. - _R. J. Mathar_, May 06 2017

%C All terms == 13 (mod 30). - _Robert Israel_, Oct 17 2023

%H Jon E. Schoenfield, <a href="/A078956/b078956.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Robert Israel)

%e 43 is in the sequence since 43, 47, 53, 59 and 61 are consecutive primes.

%p L:= [0$5]:

%p p:= 1: R:= NULL: count:= 0:

%p while count < 100 do

%p p:= nextprime(p);

%p L:= [L[2],L[3],L[4],L[5],p];

%p if L -~ L[1] = [0, 4, 10, 16, 18] then

%p count:= count+1;

%p R:= R, L[1];

%p fi

%p od:

%p R; # _Robert Israel_, Oct 17 2023

%t Select[Partition[Prime[Range[50000]],5,1],Differences[#]=={4,6,6,2}&][[All,1]] (* _Harvey P. Dale_, Jan 23 2021 *)

%Y Cf. A001223, A078866, A078867, A078946-A078971, A022006, A022007.

%K nonn

%O 1,1

%A _Labos Elemer_, Dec 19 2002

%E Edited by _Dean Hickerson_, Dec 20 2002