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

0,1

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

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.

Formula

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

Example

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]

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 *)

Crossrefs

Sequence in context: A113862 A244624 A343592 * A042960 A266596 A045975

Adjacent sequences: A036274 A036275 A036276 * A036278 A036279 A036280

Keyword

easy,nice,nonn

Author

N. J. A. Sloane

Extensions

More terms from David W. Wilson, Aug 30 2000

Status

approved