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A057522 a(n+1) = a(n)/2 if 2|a(n), a(n)/3 if 3|a(n), a(n)/5 if 5|a(n), a(n)/7 if 7|a(n), a(n)/11 if 11|a(n), otherwise 13*a(n)+1. 12
73, 950, 475, 95, 19, 248, 124, 62, 31, 404, 202, 101, 1314, 657, 219, 73, 950, 475, 95, 19, 248, 124, 62, 31, 404, 202, 101, 1314, 657, 219, 73, 950, 475, 95, 19, 248, 124, 62, 31, 404, 202, 101, 1314, 657, 219, 73, 950, 475, 95, 19, 248, 124, 62, 31, 404, 202 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

This is the '13x+1' map. The 'Px+1 map': if x is divisible by any prime < P then divide out these primes one at a time starting with the smallest; otherwise multiply x by P and add 1.

LINKS

Table of n, a(n) for n=0..55.

Eric Weisstein's World of Mathematics, Collatz problem

FORMULA

For n>15, a(n) = a(n-15). [Harvey P. Dale, May 02 2011]

EXAMPLE

73 -> 19*73+1 = 950, 950 = 2*5^2*19 -> 950/2 = 475, etc.

MATHEMATICA

nxt[n_]:=Which[Divisible[n, 2], n/2, Divisible[n, 3], n/3, Divisible[n, 5], n/5, Divisible[n, 7], n/7, Divisible[n, 11], n/11, True, 13n+1]; NestList[nxt, 73, 60] (* Harvey P. Dale, May 02 2011 *)

CROSSREFS

Cf. A057446 (short version), A057216, A057534, A057614.

Sequence in context: A296024 A254136 A123811 * A320205 A305549 A320214

Adjacent sequences: A057519 A057520 A057521 * A057523 A057524 A057525

KEYWORD

nonn

AUTHOR

Murad A. AlDamen (Divisibility(AT)yahoo.com), Oct 17 2000

STATUS

approved

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Last modified December 2 14:15 EST 2022. Contains 358510 sequences. (Running on oeis4.)