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).

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

Author

N. J. A. Sloane

Keywords

• nonn

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

Crossrefs

Cf. A001549.

Programs

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 *)

Formula

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

Extensions

Edited by Robert G. Wilson v, Aug 18 2002

More terms from Jean-François Alcover, Feb 06 2016