A000232 Construct a triangle as in A036262. Sequence is one less than the position of the first number larger than 2 in the n-th row (n-th difference). (Formerly M2718 N1089)

3, 8, 14, 14, 25, 24, 23, 22, 25, 59, 98, 97, 98, 97, 174, 176, 176, 176, 176, 291, 290, 289, 740, 874, 873, 872, 873, 872, 871, 870, 869, 868, 867, 866, 2180, 2179, 2178, 2177, 2771, 2770, 2769, 2768, 2767, 2766, 2765, 2764, 2763, 2763, 2763, 2763, 3366, 4208, 4207

Offset

1,1

Comments

Related to Gilbreath conjecture.

References

W. Sierpiński, A Selection of Problems in the Theory of Numbers. Macmillan, NY, 1964, p. 35.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

T. D. Noe, Table of n, a(n) for n=1..274

Chris Caldwell, Gilbreath's conjecture

Albert N. Debono, NUMBERS AND COMPUTERS (11)

R. B. Killgrove and K. E. Ralston, On a conjecture concerning the primes, Math. Comp., 13 (1959), 121-122.

Eric Weisstein's World of Mathematics, Gilbreath's Conjecture

Index entries for primes, gaps between

Formula

a(n) = A036277(n) - 1. - T. D. Noe, Feb 03 2007

Maple

A000232 := proc(n)
    local k;
    for k from 1 do
        if A036262(n, k) > 2 then
            return k-1 ;
        end if;
    end do:
end proc:
seq(A000232(n), n=1..40) ; # R. J. Mathar, May 10 2023

Mathematica

max = 10^4; triangle = NestList[Abs[Differences[#]] &, Prime[Range[max]], max]; a[n_] := (p = Position[triangle[[n + 1]], k_ /; k > 2, 1, 1]; If[p == {}, Nothing, p[[1, 1]] - 1]); Table[a[n], {n, 1, Sqrt[max]}] (* Jean-François Alcover, Feb 06 2016 *)

Crossrefs

Cf. A001549.

Sequence in context: A366071 A305179 A106386 * A361363 A067789 A225400

Adjacent sequences: A000229 A000230 A000231 * A000233 A000234 A000235

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Edited by Robert G. Wilson v, Aug 18 2002

More terms from Jean-François Alcover, Feb 06 2016

Status

approved