

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.


4



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
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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



