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Distance between k*(n-th prime) and next prime, k=4 case.
3

%I #4 Nov 12 2014 12:50:45

%S 3,1,3,1,3,1,3,3,5,11,3,1,3,1,3,11,3,7,1,9,1,1,5,3,1,5,7,3,3,5,1,17,9,

%T 1,3,3,3,1,5,9,3,3,5,1,9,1,9,15,3,3,5,11,3,5,3,9,11,3,1,5,19,9,1,5,7,

%U 9,3,13,11,3,11,3,3,1,7,11,3,9,3,1,17,9,9,1,3,5,5,3,3,9,3,15,1,9,1,5,3,3,7

%N Distance between k*(n-th prime) and next prime, k=4 case.

%C Other cases: k=1 A001223 Differences between consecutive primes, k=2 A059787, k=3 A111735, k=5 A111737, k=6 A111738, k=7 A111739, k=8 A111740, k=9 A111741, k=10 A111742.

%e a(1)=3 because prime(1)=2 and 4*2+3=11

%e (prime).

%t dbkn[n_]:=Module[{t=4*Prime[n]},NextPrime[t]-t]; Array[dbkn,100] (* _Harvey P. Dale_, Nov 12 2014 *)

%Y Cf. A001223, A059787, A111735, A111737, A111738, A111739, A111740, A111741, A111742.

%K nonn

%O 1,1

%A _Zak Seidov_, Nov 18 2005