A073436 Smallest k such that k mod pi(k) = n.

2, 3, 5, 7, 16, 21, 22, 25, 26, 29, 32, 65, 66, 70, 77, 78, 82, 86, 87, 88, 92, 93, 94, 95, 99, 106, 116, 117, 118, 119, 218, 219, 220, 221, 222, 247, 248, 249, 250, 255, 256, 261, 262, 267, 268, 289, 290, 291, 292, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306

Offset: 0

Author

Labos Elemer, Jul 31 2002

Keywords

• nonn

Comments

a(n) > a(n-1) except for 68, 180, 1051, 6454, 6456, 6459, 40073, 40078, ..., . - Robert G. Wilson v, Feb 24 2023

Examples

			Remainder 7 appears first as 25 mod pi(25) = 25 mod 9 = 7, so a(7) = 25.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000720, A038625, A057809, A065134, A073435, A073437, A360789.

Programs

Maple

with(numtheory); f:=proc(n) local i,j,k; for i from 2 to 10000 do if i mod pi(i) = n then RETURN(i); fi; od: RETURN(-1); end; # N. J. A. Sloane, Sep 01 2008

Mathematica

a = Compile[{{n, Integer}}, Block[{k = 2}, While[ Mod[k, PrimePi@ k] != n, k++]; k]]; Array[a, 59, 0] (* _Robert G. Wilson v, Feb 24 2023 *)

PARI

a(n)={my(q=0, k=2);forprime(p=3, oo, q++; while(kAndrew Howroyd, Feb 23 2023

Formula

a(n) = Min{k: k mod A000720(k) = n} = Min{k: A065134(k) = n}.

Extensions

a(0) from Robert G. Wilson v, Feb 23 2023