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A094501 Smallest number that requires n iterations of the sum of digits of the divisors (A034690) to reach 15.

%I A094501 #30 Dec 21 2024 22:11:14
%S A094501 15,8,7,4,3,2,19,12,6,5,13,9,10,16,30,18,34,36,66,162,924,71820,
%T A094501 127005777360
%N A094501 Smallest number that requires n iterations of the sum of digits of the divisors (A034690) to reach 15.
%H A094501 Eric Angelini et al., <a href="/A086793/a086793.txt">List the dividers [sic], sum the digits</a>, lost messages reconstructed by _N. J. A. Sloane_, Dec 21 2024
%e A094501 a(0)=15 trivially because 15 is reached in no steps (number of steps is 0);
%e A094501 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);
%e A094501 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);
%e A094501 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);
%e A094501 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.
%e A094501 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
%t A094501 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 *)
%o A094501 (Haskell)
%o A094501 import Data.List (elemIndex); import Data.Maybe (fromJust)
%o A094501 a094501 = (+ 2) . fromJust . (`elemIndex` a086793_list)
%o A094501 -- _Reinhard Zumkeller_, Nov 08 2015
%o A094501 (PARI) A094501(n)=for(k=2, 9e9, A086793(k)==n&&return(k)) \\ _M. F. Hasler_, Nov 08 2015
%Y A094501 Cf. A086793, A095347, A119397.
%Y A094501 See A260060 for another variant.
%K A094501 base,more,nonn
%O A094501 0,1
%A A094501 _Jason Earls_, Jun 05 2004
%E A094501 Examples provided by _Zak Seidov_, May 16 2006
%E A094501 Edited by _N. J. A. Sloane_ at the suggestion of _Andrew S. Plewe_, May 10 2007
%E A094501 a(22) found by exhaustive search by _Sean A. Irvine_, Oct 04 2009
%E A094501 a(22) corrected by _Donovan Johnson_ and _Sean A. Irvine_