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

Author

Labos Elemer, Oct 15 2001

Keywords

• nonn

Comments

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

Values satisfying A065133(x) = 1.

Examples

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

Links

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

Crossrefs

Cf. A000040, A000720, A065133.

Programs

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 *)

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