A065135 Numbers m such that prime(m) = pi(m)*k + 1 for some k.

3, 4, 6, 7, 10, 11, 14, 21, 37, 45, 47, 53, 55, 63, 75, 81, 101, 115, 121, 125, 136, 183, 209, 230, 271, 313, 319, 327, 348, 377, 399, 425, 460, 575, 581, 738, 786, 792, 850, 881, 917, 1076, 1110, 1152, 1246, 1519, 1740, 2062, 2074, 2119, 2144, 2327, 2361

Offset

1,1

Comments

Solutions to A000040(x) mod A000720(x) = 1.

Values satisfying A065133(x) = 1.

Links

Amiram Eldar, Table of n, a(n) for n = 1..220

Example

m = 581 is a term because prime(581) = 4211 = 106*40 + 1 = 40*pi(581) + 1.

Mathematica

seq[lim_] := Module[{r = Range[2, lim], p}, p = PrimePi[r]; 1 + Position[Mod[Prime[r], p], 1] // Flatten]; seq[2400] (* Amiram Eldar, Mar 13 2025 *)

Prog

(PARI) isok(m) = if (m>1, prime(m) % primepi(m) == 1); \\ Michel Marcus, Mar 04 2022
(PARI) list(lim) = {my(k = 1); forprime(p = 3, lim, k++; if(p % primepi(k) == 1, print1(k, ", "))); } \\ Amiram Eldar, Mar 13 2025

Crossrefs

Cf. A000040, A000720, A065133.

Sequence in context: A047297 A183233 A191926 * A229792 A101299 A143837

Adjacent sequences: A065132 A065133 A065134 * A065136 A065137 A065138

Keyword

nonn

Author

Labos Elemer, Oct 15 2001

Status

approved