A340908 Primitive numbers m without zero digits such that pod(m + pod(m)) = pod(m) where pod is the product of digits, A007954.

28, 214, 239, 266, 318, 326, 364, 494, 497, 563, 598, 613, 637, 695, 819, 2114, 2139, 2168, 2285, 2313, 2356, 2369, 2419, 2594, 2639, 2791, 3118, 3126, 3148, 3213, 3235, 3238, 3259, 3354, 3365, 3561, 3698, 3786, 4138, 4145, 4188, 4219, 4338, 4346, 4353, 4368, 4395

Offset: 1

Author

Bernard Schott, Jan 31 2021

Keywords

• nonn
• base

Comments

When a number k belongs to A327750, the integer 111..11//k obtained by concatenation of 111..11 and k is another term; hence, there exist primitive terms as 28, 214, 239, ... that are listed in this sequence.

Equivalently, terms of A327750 that do not begin with 1.

Examples

			pod(28 + pod(28)) = pod(28 + 2*8) = pod(28 + 16) = pod(44) = 4*4 = 16 = pod(28), hence 28 that does not begin with 1 is a term.
		

References

• Roman Fedorov, Alexei Belov, Alexander Kovaldzhi, and Ivan Yashchenko, Moscow-Mathematical Olympiads, 2000-2005, Level A, Problem 2, 2003; MSRI, 2011, pp. 15 and 97.

Links

• Index to sequences related to Olympiads.

Crossrefs

Cf. A007954, A247888, A340907.

Subsequence of A327750.

Programs

Mathematica

pod[n_] := Times @@ IntegerDigits[n]; q[n_] := First[IntegerDigits[n]] > 1 && (p = pod[n]) > 0 && pod[n + p] == p; Select[Range[5000], q] (* Amiram Eldar, Jan 31 2021 *)

PARI

isok(n) = my(d = digits(n), p); vecmin(d) && ((d[1]!=1) && p=vecprod(d)) && (vecprod(digits(n+p)) == p); \\ Michel Marcus, Feb 01 2021