A121561 The number of iterations of "subtract the largest prime less than or equal to the current value" to go from n to the limiting value 0 or 1.

0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 1, 1, 1, 1, 2

Offset

1,9

Comments

Number of steps to go from n to A121559(n).

The sequence has the form of blocks of numbers; see A121562 for the lengths of those blocks.

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..100000

Example

a(9) = 2 because there are 2 steps in going from 9 to 0 in A121559: 9 mod 7 = 2 and 2 mod 2 = 0.

Mathematica

LrgstPrm[n_] := Block[{k = n}, While[ !PrimeQ@ k, k-- ]; k]; f[n_] := Block[{c = 0, d = n}, While[d > 1, d = d - LrgstPrm@d; c++ ]; c]; Array[f, 105] (* Robert G. Wilson v, Feb 29 2008 *)

Prog

(Python)
from sympy import prevprime
def a(n): return 0 if n == 0 or n == 1 else 1 + a(n - prevprime(n+1))
print([a(n) for n in range(1, 106)]) # Michael S. Branicky, Jul 26 2022

Crossrefs

Cf. A121559, A064722, a(n)=1: A093515, a(n)=2: A093513, a(n)=3: A138026, a(n)=4: A138027.

Sequence in context: A328483 A321856 A175078 * A078772 A088018 A204909

Adjacent sequences: A121558 A121559 A121560 * A121562 A121563 A121564

Keyword

easy,nonn

Author

Kerry Mitchell, Aug 07 2006

Status

approved