A094501 - OEIS

A094501

Smallest number that requires n iterations of the sum of digits of the divisors (A034690) to reach 15.

15, 8, 7, 4, 3, 2, 19, 12, 6, 5, 13, 9, 10, 16, 30, 18, 34, 36, 66, 162, 924, 71820, 127005777360

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OFFSET

0,1

LINKS

Eric Angelini et al., List the dividers [sic], sum the digits, lost messages reconstructed by N. J. A. Sloane, Dec 21 2024

EXAMPLE

a(0)=15 trivially because 15 is reached in no steps (number of steps is 0);

a(1)=8 because divisors of 8 are 1,2,4,8 with sum of digits = 15 hence 15 is reached in 1 steps (number of steps is 1);

a(2)=7 because divisors of 7 are 1,7 with sum of digits =8 and we need another one step to reach 15 (number of steps is 2);

a(3)=4 because divisors of 4 are 1,2,4 with sum of digits =7 and we need another two steps to reach 15 (number of steps is 3);

a(20)=924 because starting with 924 we have the trajectory 924, 168, 102, 36, 46, 18, 30, 27, 22, 9, 13, 5, 6, 12, 19, 11, 3, 4, 7, 8, 15 reaching 15 in 20 steps.

a(21)=71820 because starting with 71820 we have the trajectory 71820, 1104, 168, 102, 36, 46, 18, 30, 27, 22, 9, 13, 5, 6, 12, 19, 11, 3, 4, 7, 8, 15 reaching 15 in 21 steps. - Sean A. Irvine, Oct 04 2009

MATHEMATICA

f[n_] := Block[{i = 0}, NestWhile[(i++; Plus @@ Flatten@ IntegerDigits@ Divisors@#) &, n, # != 15 &]; i]; t = Table[0, {100}]; Do[ a = f[n]; If[ t[[a]] < 101 && t[[a]] == 0, t[[a]] = n], {n, 2, 10^8}]; t (* Robert G. Wilson v, May 16 2006 *)

PROG

(Haskell)

import Data.List (elemIndex); import Data.Maybe (fromJust)

a094501 = (+ 2) . fromJust . (`elemIndex` a086793_list)

-- Reinhard Zumkeller, Nov 08 2015

(PARI) A094501(n)=for(k=2, 9e9, A086793(k)==n&&return(k)) \\ M. F. Hasler, Nov 08 2015

CROSSREFS

Cf. A086793, A095347, A119397.

See A260060 for another variant.

Sequence in context: A305998 A103241 A194707 * A320572 A090636 A126892

Adjacent sequences: A094498 A094499 A094500 * A094502 A094503 A094504

KEYWORD