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

7, 5, 251, 353, 137, 2393, 109, 1931, 1753, 883, 3733, 7351, 12007, 2969, 8887, 27697, 1321, 22811, 38377, 62987, 183823, 15679, 124001, 180563, 45887, 48677, 100847, 178693, 152993, 557087, 34057, 367949, 294551, 134507, 173357, 1802407, 531359, 1134311, 933067

Offset

1,1

Comments

The sequence is generalizable with primes starting a sequence of 2k consecutive odd primes.

Conjecture: a(n) exists for all n>0.

Links

Table of n, a(n) for n=1..39.

Example

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.

Maple

with(numtheory):nn:=500000:l:=2:T:=array(1..2*l-1)):
for n from 1 to 35 do:ii:=0:
  for k from 1 to nn while(ii=0) do:
      lst:={}:lst1:={}:
       for m from 1 to 2*l do:
        lst:=lst union {ithprime(k+m-1)}
       od:
         for p from 1 to 2*l do:
          lst1:=lst1 union {lst[p]+lst[2*l-p+1]}
         od:
            n0:=nops(lst1):
            if n0=1
            then
           for a from 1 to 2*l-1 do:
           T[a]:=lst[a+1]-lst[a]:
           od:
           if T[2]=2*n then ii:=1:printf(`%d, `, lst[1]):
           else fi :fi:
           od :
          od:

Prog

(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

Crossrefs

Cf. A001223, A055380, A055381, A055382, A175309.

Sequence in context: A012878 A300452 A302201 * A003299 A198677 A154017

Adjacent sequences: A263168 A263169 A263170 * A263172 A263173 A263174

Keyword

nonn

Author

Michel Lagneau, Oct 11 2015

Status

approved