A271220 Concatenate sum of digits of previous term and product of digits of previous term, starting with 6.

6, 66, 1236, 1236, 1236, 1236, 1236, 1236, 1236, 1236, 1236, 1236, 1236, 1236, 1236, 1236, 1236, 1236, 1236, 1236, 1236, 1236, 1236, 1236, 1236, 1236, 1236, 1236, 1236, 1236, 1236, 1236, 1236, 1236, 1236, 1236, 1236, 1236, 1236, 1236, 1236, 1236, 1236, 1236, 1236, 1236, 1236, 1236, 1236, 1236

Offset: 0

Author

Sander Claassen, Apr 02 2016

Keywords

• nonn
• easy
• base

Comments

Each term is created by calculating the sum of the digits of the previous number, and the product of its digits. The results are concatenated to give the new number. Starting with 6, the second number is 66. The third number is generated as follows: 6+6 = 12, 6*6 = 36, which gives 1236. After that, the numbers remain unchanged, because 1+2+3+6 = 12 and 1x2x3x6 = 36, so combined 1236 again.

For more information, see A380873 (the iterated function), A380872 (all trajectories), A062237 (fixed points). - M. F. Hasler, Apr 02 2025

Links

• Index entries for linear recurrences with constant coefficients, signature (1).

Crossrefs

Cf. A380873 (the iterated function), A007953 (sum of digits), A007954 (product of digits), A380872 (all trajectories), A062237 (fixed points).

Programs

Mathematica

NestList[FromDigits[Flatten@ {IntegerDigits@ Total@ #, IntegerDigits@ If[Length@ # == 1, #, Times @@ #]}] &@ IntegerDigits@ # &, 6, 50] (* Michael De Vlieger, Apr 02 2016 *)

PARI

A380872_row(6) \\ M. F. Hasler, Apr 02 2025

Formula

a(n) = 1236 for all n > 2. - M. F. Hasler, Apr 02 2025

Extensions

Offset changed to 0 by M. F. Hasler, Apr 02 2025