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

1,1

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.

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

Table of n, a(n) for n=1..47.

Index to sequences related to Olympiads.

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A007954, A247888, A340907.

Subsequence of A327750.

Sequence in context: A244944 A155466 A053135 * A297614 A249710 A269621

Adjacent sequences: A340905 A340906 A340907 * A340909 A340910 A340911

Keyword

nonn,base

Author

Bernard Schott, Jan 31 2021

Status

approved