A090532 Let f(n) = n - pi(n) = A062298(n). Then a(n) = least number of steps such that f(f(...(n))) = 1.

0, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9

Offset

1,4

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Example

a(10) = 3, 10 -> 6 -> 3 -> 1.
a(100) = 9; f(100) = 100 - 25 = 75, f(75) = 75 - 21 = 54, f(54) = 54 - 16 = 38, f(38) = 38 - 12 = 26, f(26) = 26 - 9 = 17, f(17) = 17 - 7 = 10, f(10) = 10 - 4 = 6, f(6) = 6 - 3 = 3, f(3) = 3 - 2 = 1.

Mathematica

pi[n_] := pi[n] = PrimePi[n];
A090532[n_] := Length[FixedPointList[# - pi[#] &, n]] - 2;
Array[A090532, 100] (* Paolo Xausa, Dec 13 2025 *)

Prog

(PARI) a(n) = my(nb=0); while(n != 1, nb++; n -= primepi(n)); nb; \\ Michel Marcus, Dec 14 2025

Crossrefs

Cf. A025003, A062298.

Sequence in context: A278163 A347635 A260999 * A003058 A000194 A168255

Adjacent sequences: A090529 A090530 A090531 * A090533 A090534 A090535

Keyword

nonn

Author

Amarnath Murthy, Dec 07 2003

Extensions

Corrected and extended by Sam Handler (sam_5_5_5_0(AT)yahoo.com), Dec 11 2004

a(1) = 0 prepended by Paolo Xausa, Dec 13 2025

Status

approved