A031157 - OEIS

A031157

Numbers that are both lucky and prime.

3, 7, 13, 31, 37, 43, 67, 73, 79, 127, 151, 163, 193, 211, 223, 241, 283, 307, 331, 349, 367, 409, 421, 433, 463, 487, 541, 577, 601, 613, 619, 631, 643, 673, 727, 739, 769, 787, 823, 883, 937, 991, 997, 1009, 1021, 1039, 1087, 1093, 1117, 1123

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OFFSET

1,1

COMMENTS

A010051(a(n))*A145649(a(n)) = 1. - Reinhard Zumkeller, Oct 19 2008

Conjecture: This sequence is infinite. - Ahmad J. Masad, Feb 17 2020

Conjecture: If this sequence is infinite, then there exists a minimum sufficiently large integer k, such that for all a(n) > k, there exists a positive integer x and there exists m>n such that x(x-1) < a(n) < x^2 and x^2 < a(m) < x(x+1). This conjecture is similar to Oppermann's conjecture. - Ahmad J. Masad, Jun 23 2020

LINKS

T. D. Noe, Table of n, a(n) for n = 1..10000

Marthinus Michael Dreeckmeier, On the Fundamental Arithmetical Structure and Distribution of Lucky Numbers, arXiv:2511.11657 [math.GM], 2025. See p. 11.

Wikipedia, Lucky prime

MATHEMATICA

luckies = Range[1, 1248, 2]; i = 2; While[ i <= (len = Length@luckies) && (k = luckies[[i]]) <= len, luckies = Drop[luckies, {k, len, k}]; i++ ]; Select[luckies, PrimeQ@# &] (* Robert G. Wilson v, May 12 2006 *)

CROSSREFS

Intersection of A000040 and A000959.

Cf. A055728, A016921.

Sequence in context: A249378 A136060 A023227 * A049488 A136051 A100750

Adjacent sequences: A031154 A031155 A031156 * A031158 A031159 A031160

KEYWORD

nonn

AUTHOR

Patrick De Geest

STATUS

approved