A079011 - OEIS

A079011

Least prime p introducing prime-difference pattern {d, 2*d}, where d = 2*n, i.e., {p, p+2*n, p+2*n+4*n} = {p, p+2*n, p+6*n} are consecutive primes.

5, 397, 503, 1823, 1627, 8317, 5939, 94153, 69539, 83117, 444187, 177019, 428873, 1179649, 955511, 1625027, 2541289, 1290683, 19856363, 12183757, 5412091, 23374859, 27248701, 38235013, 21369059, 34718041, 84120737, 59859131, 125283913, 44155159, 70136597, 324954127

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..32.

EXAMPLE

For n=3, d = 2*n = 6, d-pattern = {6, 12}, a(3) = 503, first corresponding prime triple is {503, 509, 521}.

MATHEMATICA

d[x_] := Prime[x+1]-Prime[x]; t=Table[0, {70}]; Do[s=d[n]/2; If[(d[n+1]==4*s)&&(t[[s]]==0), t[[s]]=Prime[n]], {n, 2, 100000}]; t

PROG

(PARI) a(n) = my(p=5, q=3, r=2); until(r+2*n==q&&q+4*n==p, r=q; q=p; p=nextprime(p+1)); r; \\ Jinyuan Wang, Feb 10 2021

CROSSREFS