A383591 Smallest prime p where the absolute difference of the gaps to the adjacent primes exceeds n*log(p).

7, 113, 1327, 15683, 31397, 31397, 360653, 1349533, 1357333, 17051887, 20831323, 47326913, 436273291, 3842610773, 3842610773, 22367084959, 25056082087, 25056082087, 304599509051, 1346294310749

Offset

1,1

Links

Table of n, a(n) for n=1..20.

J. M. Flagg, Louis H. Kauffman, and Divyamaan Sahoo, Primes Between Squares - Commentary on Appendix 8 of Laws Of Form, arXiv:2511.05603 [math.NT], 2025. See p. 52.

Example

a(3) = 1327 because we have abs(1321 - 2*1327 + 1361) = 28, which is greater than 3*log(1327) ≈ 21.57, and no smaller prime meets this condition.

Crossrefs

Cf. A036263, A383215, A383216.

Sequence in context: A081531 A142537 A084974 * A156240 A152927 A064330

Adjacent sequences: A383588 A383589 A383590 * A383592 A383593 A383594

Keyword

nonn,hard,more

Author

Jean-Marc Rebert, May 03 2025

Status

approved