A073437 -id:A073437 - cp's OEIS frontend

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

Labos Elemer, Jul 31 2002

nonn

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

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

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

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

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

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 *)

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

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

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

A073438 Remainder of division G[n]/Pi[n], where G[n] is the number of composites not exceeding n.

Original entry on oeis.org

0, 0, 1, 1, 2, 2, 3, 0, 1, 0, 1, 0, 1, 2, 3, 2, 3, 2, 3, 4, 5, 4, 5, 6, 7, 8, 0, 8, 9, 8, 9, 10, 0, 1, 2, 0, 1, 2, 3, 1, 2, 0, 1, 2, 3, 1, 2, 3, 4, 5, 6, 4, 5, 6, 7, 8, 9, 7, 8, 6, 7, 8, 9, 10, 11, 9, 10, 11, 12, 10, 11, 9, 10, 11, 12, 13, 14, 12, 13, 14, 15, 13, 14, 15, 16, 17, 18, 16, 17, 18

Offset: 2

Labos Elemer, Jul 31 2002

nonn

			n=100: G[100]=100-Pi[100]-1=100-25-1=74, Pi[100]=25, remainder=a(100)=Mod[74,25]=24.

Harvey P. Dale, Table of n, a(n) for n = 2..1000

Cf. A065855, A000720, A073437.

Table[Mod[w-PrimePi[w]-1, PrimePi[w]], {w, 1, 128}]
With[{nn=100},Mod[#[[1]]-#[[2]]-1,#[[2]]]&/@Thread[{Range[2,nn],PrimePi[Range[2,nn]]}]] (* Harvey P. Dale, Feb 26 2025 *)

a(n)=Mod[A065855(n), A000720(n)]=Mod[n-Pi[n]-1, Pi[n]] for n>1.

cp's OEIS Frontend

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

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