A233550 Gap g between 3 consecutive primes for the smallest k such that 6^n+k, 6^n+k+g, 6^n+k+2*g are consecutive primes in arithmetic progression.

6, 6, 6, 6, 12, 6, 18, 12, 6, 24, 18, 12, 6, 18, 12, 42, 30, 12, 54, 24, 60, 30, 24, 36, 78, 18, 42, 132, 42, 24, 24, 60, 24, 72, 24, 36, 30, 6, 12, 30, 30, 120, 6, 36, 72, 30, 30, 18, 6, 60, 210, 66, 84, 30, 96, 24, 84, 6, 210, 78, 18, 228

Offset: 2

Author

Pierre CAMI, Dec 16 2013

Keywords

• nonn

Comments

Sequence starts for n=2 as no solution for n=1.

g is a multiple of 6 as otherwise 6^n+k, 6^n+k+g, or 6^n+k+2*g is divisible by 2 or 3. - Jonathan Sondow, Dec 16 2013

Examples

			6^2+11=47, 6^2+11+6=53, 6^2+11+2*6=59 are consecutive primes and k=11 is minimal, so a(2)=6. - _Jonathan Sondow_, Dec 16 2013
		

Links

• Pierre CAMI, Table of n, a(n) for n = 2..350

Crossrefs

Cf. A233546 (associated k), A233742.

Programs

PFGW

; See A233546.

Formula

a(n) = 6*A233742(n). - Jonathan Sondow, Dec 16 2013