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A247097 a(n) = least integer m such that prime(n)+m and prime(n+1)+m are prime. 2
2, 6, 6, 6, 6, 12, 18, 8, 12, 6, 6, 18, 24, 6, 8, 12, 6, 12, 30, 10, 18, 14, 12, 6, 6, 6, 30, 18, 24, 36, 20, 12, 18, 30, 6, 10, 30, 6, 18, 12, 42, 6, 30, 30, 12, 16, 6, 12, 48, 18, 30, 30, 6, 6, 8, 12, 6, 30, 30, 24, 24, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

In most cases terms are congruent to 0 mod 6. Out of the first 1000 terms, 830 are multiples of 6.

It is conjectured that a(n) always exists.

LINKS

Colin Barker, Table of n, a(n) for n = 2..10000

EXAMPLE

Offset is 2, hence first term corresponds to n=2.

For n=2, prime(n)=3,  prime(n+1)=5, m=2, and 3+2 and 5+2 are prime.

For n=3, m=6, 5+6 and 7+6 are prime.

PROG

(PARI) s=[]; for(n=2, 100, p=prime(n); q=prime(n+1); m=1; while(!(isprime(p+m)&&isprime(q+m)), m++); s=concat(s, m)); s \\ Colin Barker, Nov 18 2014

CROSSREFS

Sequence in context: A184408 A184409 A137479 * A258576 A278253 A048765

Adjacent sequences:  A247094 A247095 A247096 * A247098 A247099 A247100

KEYWORD

nonn

AUTHOR

Zak Seidov, Nov 18 2014

STATUS

approved

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Last modified February 25 14:46 EST 2018. Contains 299654 sequences. (Running on oeis4.)