A175078 Number of iterations of {r mod (max prime p < r)} needed to reach 1 or 2 starting at r = n.

0, 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

Offset

1,10

Comments

a(123) = 3 (first occurrence of value 3), a(1357324) = 4 (first occurrence of value 4). I offer a prize of 100 liters of Pilsner Urquell to the discoverer of value of first occurrence of value 5. See A175071 (natural numbers m with result 1) and A175072 (natural numbers m with result 2). See A175077 = results 1 or 2 under iterations of {r mod (max prime p < r)} starting at r = n.

Essentially the same as A121561. [R. J. Mathar, Jan 28 2010]

The function r mod (max prime p < r), which appears in the definition, equals r - (max prime p < r) = A049711(r), because p < r < 2*p by Bertrand's postulate, where p is the largest prime less than r. - Pontus von Brömssen, Jul 31 2022

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Formula

a(n) = A121561(n-1) for n >= 2, because the functions that are iterated (A049711 here, A064722 in A121561) satisfies A049711(r) = A064722(r-1) + 1. - Pontus von Brömssen, Jul 31 2022

Example

a(123) = 3; iteration procedure for n = 123: 123 mod 113 = 10, 10 mod 7 = 3, 3 mod 2 = 1.

Mathematica

Array[-1 + Length@ NestWhileList[Mod[#, NextPrime[#, -1]] &, #, Not[1 <= # <= 2] &, 1, 120] &, 105] (* Michael De Vlieger, Oct 30 2017 *)

Prog

(PARI) A175078(n) = if(n<=2, 0, 1+A175078(n%precprime(n-1))); \\ Antti Karttunen, Oct 30 2017

Crossrefs

Cf. A049711, A064722, A121559, A121561, A175071, A175072, A175077.

Sequence in context: A096285 A328483 A321856 * A121561 A078772 A088018

Adjacent sequences: A175075 A175076 A175077 * A175079 A175080 A175081

Keyword

nonn

Author

Jaroslav Krizek, Jan 23 2010

Extensions

Name shortened by Antti Karttunen, Oct 30 2017

Status

approved