A321149 a(1) = 102735, a(n) = prime(n-1)*a(n-1) but products that are not in A010784 are first reduced as in A320486 (see comments); continue until zero is reached.

102735, 2547, 7641, 38205, 267435, 2941785, 8405, 1425, 205, 4715, 1675, 192, 7104, 9164, 394052, 18520, 981560, 579124, 24, 1608, 468, 316, 296, 24568, 186, 18042, 184, 18952, 7864, 8516, 962308, 36

Offset: 1

Author

Hans Havermann, Oct 28 2018

Keywords

• nonn
• fini
• full
• base

Comments

At each step, integers that contain duplicated digits are reduced to terms of A010784 by erasing all digits that appear more than once and bunching up the digits that remain. Leading zeros are ignored and any number that disappears entirely becomes 0. See A320486.

102735 is the smallest of 785 A010784 terms that result in a 362-term sequence, the longest possible.

Examples

			2 * 102735 = [205470] => 2547
3 * 2547 = 7641
5 * 7641 = 38205
7 * 38205 = 267435
11 * 267435 = 2941785
13 * 2941785 = [38243205] => 8405
17 * 8405 = [142885] => 1425
19 * 1425 = [27075] => 205
...
2417 * 40 = [96680] => 980
2423 * 980 = [2374540] => 23750
2437 * 23750 = [57878750] => 0
		

Links

• Hans Havermann, Table of n, a(n) for n = 1..362
• Hans Havermann, What's so special about 102735?

Crossrefs

Cf. A010784, A321148, A320486.