cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A340908 #21 Apr 03 2023 15:05:47
%S A340908 28,214,239,266,318,326,364,494,497,563,598,613,637,695,819,2114,2139,
%T A340908 2168,2285,2313,2356,2369,2419,2594,2639,2791,3118,3126,3148,3213,
%U A340908 3235,3238,3259,3354,3365,3561,3698,3786,4138,4145,4188,4219,4338,4346,4353,4368,4395
%N A340908 Primitive numbers m without zero digits such that pod(m + pod(m)) = pod(m) where pod is the product of digits, A007954.
%C A340908 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.
%C A340908 Equivalently, terms of A327750 that do not begin with 1.
%D A340908 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.
%H A340908 <a href="/index/O#Olympiads">Index to sequences related to Olympiads</a>.
%e A340908 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.
%t A340908 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 *)
%o A340908 (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
%Y A340908 Cf. A007954, A247888, A340907.
%Y A340908 Subsequence of A327750.
%K A340908 nonn,base
%O A340908 1,1
%A A340908 _Bernard Schott_, Jan 31 2021