cp's OEIS Frontend

A277729 Irregular triangle read by rows: T(n,k) = number of times a gap of k occurs between the first n successive primes.

%I A277729 #14 Nov 17 2016 05:19:25
%S A277729 1,1,1,1,2,1,2,0,1,1,3,0,1,1,3,0,2,1,4,0,2,1,4,0,3,1,4,0,3,0,1,1,5,0,
%T A277729 3,0,1,1,5,0,3,0,2,1,5,0,4,0,2,1,6,0,4,0,2,1,6,0,5,0,2,1,6,0,5,0,3,1,
%U A277729 6,0,5,0,4,1,7,0,5,0,4,1,7,0,5,0,5,1,7,0,6,0,5,1,8,0,6,0,5,1,8,0,6,0,6,1,8,0,7,0,6,1,8,0,7,0,7,1,8,0,7,0,7,0,1,1,8,0,8,0,7,0,1,1,9,0
%N A277729 Irregular triangle read by rows: T(n,k) = number of times a gap of k occurs between the first n successive primes.
%H A277729 Robert Israel, <a href="/A277729/b277729.txt">Table of n, a(n) for n = 2..10032</a> (rows 2 to 410, flattened)
%e A277729 Triangle begins:
%e A277729 1,
%e A277729 1, 1,
%e A277729 1, 2,
%e A277729 1, 2, 0, 1,
%e A277729 1, 3, 0, 1, <- gaps in 2,3,5,7,11,13 are 1, 2 (3 times), 4 (once)
%e A277729 1, 3, 0, 2,
%e A277729 1, 4, 0, 2,
%e A277729 1, 4, 0, 3,
%e A277729 1, 4, 0, 3, 0, 1,
%e A277729 1, 5, 0, 3, 0, 1,
%e A277729 1, 5, 0, 3, 0, 2,
%e A277729 1, 5, 0, 4, 0, 2,
%e A277729 1, 6, 0, 4, 0, 2,
%e A277729 1, 6, 0, 5, 0, 2,
%e A277729 1, 6, 0, 5, 0, 3,
%e A277729 1, 6, 0, 5, 0, 4,
%e A277729 1, 7, 0, 5, 0, 4,
%e A277729 1, 7, 0, 5, 0, 5,
%e A277729 1, 7, 0, 6, 0, 5,
%e A277729 1, 8, 0, 6, 0, 5,
%e A277729 ...
%p A277729 N:= 30: # for rows 2 to N
%p A277729 res:= 1; p:= 3; R:= <1>;
%p A277729 for n from 2 to N do
%p A277729   pp:= nextprime(p);
%p A277729   d:= pp - p;
%p A277729   p:= pp;
%p A277729   if d <= LinearAlgebra:-Dimension(R) then
%p A277729     R[d]:= R[d]+1
%p A277729   else
%p A277729     R(d):= 1
%p A277729   fi;
%p A277729   res:= res, op(convert(R,list));
%p A277729 od:
%p A277729 res;  # _Robert Israel_, Nov 16 2016
%Y A277729 Cf. A277730, A213930.
%K A277729 nonn,tabf
%O A277729 2,5
%A A277729 _N. J. A. Sloane_, Nov 06 2016