A368364 a(n) = number of s with n^k-n^2 <= s <= n^k-1, k >= 3, such that a comma sequence in base n with initial term s will not reach n^k.

0, 1, 2, 4, 5, 7, 8, 11, 12, 14, 16, 18, 20, 23, 24, 26, 29, 31, 33, 36, 38, 40, 42, 45, 47, 51, 52, 54, 58, 60, 61, 65, 67, 71, 73, 75, 77, 81, 83, 85, 89, 91, 93, 98, 100, 102, 104, 107, 110, 114, 116, 118, 122, 125, 127, 131, 133, 135, 139, 141, 143, 149, 150, 154

Offset

2,3

Comments

Conjectured to have g.f. (Sum_{n>=1} x^((n^2+3*n)/2)/(1-x^n) - x^2)/(1-x). [Corrected by N. J. A. Sloane, May 14 2024]

a(n) is independent of k provided k >= 3.

This is conjectured to equal A368363(n) - 1. Normally that would be enough to rule out this sequence. However, it is included because it is at present the only one of the nearly 100 OEIS entries based on comma sequences which has a connection with a sequence not connected with comma sequences.

(In the (virtual) graph that shows connections between OEIS entries, this sequence is the sole node at present that connects the component containing A121805 to the rest of the graph.)

Links

Table of n, a(n) for n=2..65.

Eric Angelini, Michael S. Branicky, Giovanni Resta, N. J. A. Sloane, and David W. Wilson, The Comma Sequence: A Simple Sequence With Bizarre Properties, arXiv:2401.14346, Youtube

Example

In base 10, a(10) = 8 values of s hit a landmine before reaching safety.

Crossrefs

Cf. A121805, A136107, A368363.

Sequence in context: A188298 A376116 A289129 * A290334 A206285 A356449

Adjacent sequences: A368361 A368362 A368363 * A368365 A368366 A368367

Keyword

nonn

Author

N. J. A. Sloane, Jan 19 2024

Status

approved