A118741 Primes for which the weight as defined in A117078 is 7.

67, 83, 167, 193, 251, 277, 433, 487, 503, 587, 601, 613, 727, 823, 907, 1063, 1217, 1231, 1553, 1663, 1777, 1861, 1873, 1973, 1987, 2083, 2281, 2293, 2351, 2377, 2393, 2797, 2897, 3217, 3343, 3541, 3847, 4073, 4283, 4451, 4507, 4591, 4813, 4871, 5081

Offset: 1

Author

Rémi Eismann, May 22 2006; May 27 2006; May 04 2007

Keywords

• nonn

Comments

The gap as defined in A001223 of this prime numbers is 4 or 6.

The prime numbers in this sequence are of the form (14i-1) (if gap=6) or (14i-3) (if gap=4) with i=(level(n)+1)/2, level(n) defined in A117563.

Links

• Remi Eismann, Table of n, a(n) for n=1..10000

Crossrefs

Cf. A117078, A117563, A118922, A118924.

Programs

Mathematica

f[n_] := Block[{a, p = Prime[n], np = Prime[n + 1]}, a = Min[Select[Divisors[2*p - np], #1 > np - p & ]]; If[a == Infinity, 0, a]]; Prime@ Select[ Range@695, f@# == 7 &] (* Robert G. Wilson v, May 26 2006 *)

Formula

A117078 : a(n) = smallest k such that prime(n+1) = prime(n) + (prime(n) mod k), or 0 if no such k exists. prime(n) for which k=7.

Extensions

More terms from Robert G. Wilson v, May 26 2006