A247097 a(n) = least integer m such that prime(n)+m and prime(n+1)+m are prime.

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

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.

Mathematica

lm[{a_, b_}]:=Module[{m=2}, While[!PrimeQ[a+m]||!PrimeQ[b+m], m+=2]; m]; lm/@ Partition[ Prime[Range[2, 70]], 2, 1] (* Harvey P. Dale, Oct 02 2018 *)

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: A184409 A137479 A304363 * A258576 A278253 A294961

Adjacent sequences: A247094 A247095 A247096 * A247098 A247099 A247100

Keyword

nonn

Author

Zak Seidov, Nov 18 2014

Status

approved