A036277 Position of first term > 2 in n-th row of Gilbreath array shown in A036262.

2, 4, 9, 15, 15, 26, 25, 24, 23, 26, 60, 99, 98, 99, 98, 175, 177, 177, 177, 177, 292, 291, 290, 741, 875, 874, 873, 874, 873, 872, 871, 870, 869, 868, 867, 2181, 2180, 2179, 2178, 2772, 2771, 2770, 2769, 2768, 2767, 2766, 2765, 2764, 2764, 2764, 2764, 3367

Offset: 0

Author

N. J. A. Sloane

Keywords

• easy
• nice
• nonn

Comments

Gilbreath's conjecture is equivalent to: A036277(n)>A213014(n)+2 for all n>0. See A036262 for a proof. - M. F. Hasler, Jun 02 2012

Examples

			Row 1 of A036262 is 1 2 2 4 2 4 2 4 ... so a(1) = 4.
[N.B.: While the first row of the table A036261 contains the absolute first differences of the primes, table A036262 starts with the primes themselves in the uppermost row, which is obviously here referred to as the 0th row. - _M. F. Hasler_, Jun 02 2012]
		

References

• A. S. Fraenkel and B. J. Reuter, On certain sequences of integers and prime numbers, Proc. 2nd National Conf. Data Processing, Rehovoth, Jan 1966, pp. 450-437.
• R. K. Guy, Unsolved Problems Number Theory, A10.

Links

• T. D. Noe, Table of n, a(n) for n=0..274
• A. M. Odlyzko, Iterated absolute values of differences of consecutive primes, Math. Comp., 61 (1993), pp. 373-380.

Programs

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]]]); Table[a[n], {n, 0, Sqrt[max]}] (* Jean-François Alcover, Feb 06 2016 *)

Formula

a(n) = A000232(n)+1. - R. J. Mathar, May 10 2023

Extensions

More terms from David W. Wilson, Aug 30 2000