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

Offset: 1

Author

Labos Elemer, Jan 21 2003

Keywords

• nonn

Examples

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

Crossrefs

Cf. A079012, A079013.

Programs

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

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

Extensions

Terms corrected and more terms from Jinyuan Wang, Feb 10 2021