0,1

735134400 < a(22) <= 323203999999676796. - David Wasserman (dwasserm(AT)earthlink.net), May 09 2007

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.

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 (from Robert G. Wilson v May 16 2006)

Cf. A086793, A095347.

Cf. A095347, A119397.

Sequence in context: A131876 A126070 A103241 this_sequence A090636 A126892 A139725

Adjacent sequences: A094498 A094499 A094500 this_sequence A094502 A094503 A094504

base,more,nonn

Jason Earls (zevi_35711(AT)yahoo.com), Jun 05 2004

Examples provided by Zak Seidov (zakseidov(AT)yahoo.com), May 16 2006.

Edited by njas at the suggestion of Andrew Plewe, May 10 2007