cp's OEIS Frontend

A263171 Smallest prime starting a sequence of 4 consecutive odd primes such that the center of the symmetrical gaps is 2n.

%I A263171 #9 Oct 16 2015 06:03:56
%S A263171 7,5,251,353,137,2393,109,1931,1753,883,3733,7351,12007,2969,8887,
%T A263171 27697,1321,22811,38377,62987,183823,15679,124001,180563,45887,48677,
%U A263171 100847,178693,152993,557087,34057,367949,294551,134507,173357,1802407,531359,1134311,933067
%N A263171 Smallest prime starting a sequence of 4 consecutive odd primes such that the center of the symmetrical gaps is 2n.
%C A263171 The sequence is generalizable with primes starting a sequence of 2k consecutive odd primes.
%C A263171 Conjecture: a(n) exists for all n>0.
%e A263171 a(2)=5 because the 4 consecutive primes 5, 7, 11, 13 have gaps 2, 4, 2, which is symmetric about its center 4 = 2*2.
%p A263171 with(numtheory):nn:=500000:l:=2:T:=array(1..2*l-1)):
%p A263171 for n from 1 to 35 do:ii:=0:
%p A263171   for k from 1 to nn while(ii=0) do:
%p A263171       lst:={}:lst1:={}:
%p A263171        for m from 1 to 2*l do:
%p A263171         lst:=lst union {ithprime(k+m-1)}
%p A263171        od:
%p A263171          for p from 1 to 2*l do:
%p A263171           lst1:=lst1 union {lst[p]+lst[2*l-p+1]}
%p A263171          od:
%p A263171             n0:=nops(lst1):
%p A263171             if n0=1
%p A263171             then
%p A263171            for a from 1 to 2*l-1 do:
%p A263171            T[a]:=lst[a+1]-lst[a]:
%p A263171            od:
%p A263171            if T[2]=2*n then ii:=1:printf(`%d, `,lst[1]):
%p A263171            else fi :fi:
%p A263171            od :
%p A263171           od:
%o A263171 (PARI) a(n) = {pa = 3; pb = 5; pc = 7; forprime(p=8, , if (((pc-pb) == 2*n) && ((pb-pa) == (p-pc)), return(pa)); pa = pb; pb = pc; pc = p;);} \\ _Michel Marcus_, Oct 16 2015
%Y A263171 Cf. A001223, A055380, A055381, A055382, A175309.
%K A263171 nonn
%O A263171 1,1
%A A263171 _Michel Lagneau_, Oct 11 2015