A361919 The number of primes > A000040(n) and <= (A000040(n)^c + 1)^(1/c), where c = 0.567148130202... is defined in A038458.

1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 4, 4, 3, 2, 1, 1, 3, 2, 3, 2, 3, 2, 3, 3, 3, 2, 3, 3, 3, 2, 2, 1, 3, 5, 4, 3, 3, 3, 2, 3, 3, 4, 4, 3, 3, 2, 1, 3, 3, 3, 2, 2, 4, 4, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 3, 4, 5, 4, 4, 4, 5, 5

Offset

1,7

Comments

Let c = 0.567148130202... (see A038458), the solution to 127^x - 113^x = 1. c is conjectured by Smarandache to be the smallest real number x such that A000040(n+1)^x - A000040(n)^x = 1 has a solution. This conjecture is equivalent to saying that the terms of the present sequence are always positive, but that if c were replaced by a larger real number, there would be zeros in the sequence. However, note that a(30) is not the last occurrence of 1: a(46) = a(61) = 1 as well.

Links

Hal M. Switkay, Table of n, a(n) for n = 1..665

F. Smarandache, Conjectures which generalize Andrica's conjecture, arXiv:0707.2584 [math.GM], 2007; Octogon 7:1 (1999), pp. 173-176.

Example

a(30) is the number of primes > A000040(30), which is 113, and <= (113^c + 1)^(1/c) = 127. This relatively large interval contains only the prime 127.

Crossrefs

Cf. A000040, A038458.

Sequence in context: A033182 A053797 A254011 * A372362 A002635 A275806

Adjacent sequences: A361916 A361917 A361918 * A361920 A361921 A361922

Keyword

nonn

Author

Hal M. Switkay, Mar 29 2023

Status

approved