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
Offset: 0
Examples
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
Links
- Eric Angelini et al., List the dividers [sic], sum the digits, lost messages reconstructed by _N. J. A. Sloane_, Dec 21 2024
Programs
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Haskell
import Data.List (elemIndex); import Data.Maybe (fromJust) a094501 = (+ 2) . fromJust . (`elemIndex` a086793_list) -- Reinhard Zumkeller, Nov 08 2015
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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 *) -
PARI
A094501(n)=for(k=2, 9e9, A086793(k)==n&&return(k)) \\ M. F. Hasler, Nov 08 2015
Extensions
Examples provided by Zak Seidov, May 16 2006
Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, May 10 2007
a(22) found by exhaustive search by Sean A. Irvine, Oct 04 2009
a(22) corrected by Donovan Johnson and Sean A. Irvine