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

2,1

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

Links

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

Formula

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

Example

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

Prog

See A233546.

Crossrefs

Cf. A233546 (associated k), A233742.

Sequence in context: A001734 A342373 A173067 * A092937 A285287 A285048

Adjacent sequences: A233547 A233548 A233549 * A233551 A233552 A233553

Keyword

nonn

Author

Pierre CAMI, Dec 16 2013

Status

approved