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 A277729 Irregular triangle read by rows: T(n,k) = number of times a gap of k occurs between the first n successive primes. 2
 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, 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, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,5 LINKS Robert Israel, Table of n, a(n) for n = 2..10032 (rows 2 to 410, flattened) EXAMPLE Triangle begins: 1, 1, 1, 1, 2, 1, 2, 0, 1, 1, 3, 0, 1, <- gaps in 2,3,5,7,11,13 are 1, 2 (3 times), 4 (once) 1, 3, 0, 2, 1, 4, 0, 2, 1, 4, 0, 3, 1, 4, 0, 3, 0, 1, 1, 5, 0, 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, 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, ... MAPLE N:= 30: # for rows 2 to N res:= 1; p:= 3; R:= <1>; for n from 2 to N do   pp:= nextprime(p);   d:= pp - p;   p:= pp;   if d <= LinearAlgebra:-Dimension(R) then     R[d]:= R[d]+1   else     R(d):= 1   fi;   res:= res, op(convert(R, list)); od: res;  # Robert Israel, Nov 16 2016 CROSSREFS Cf. A277730, A213930. Sequence in context: A035160 A027414 A140083 * A057985 A135387 A321104 Adjacent sequences:  A277726 A277727 A277728 * A277730 A277731 A277732 KEYWORD nonn,tabf AUTHOR N. J. A. Sloane, Nov 06 2016 STATUS approved

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Last modified December 8 11:31 EST 2021. Contains 349596 sequences. (Running on oeis4.)