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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 13 14:44 EDT 2021. Contains 345003 sequences. (Running on oeis4.)