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a(n) is the smallest number k such that A358351(k) = n.
2

%I #23 Nov 20 2022 08:46:08

%S 1,3,26,38,380,1116,12912,95131,342038,3320210,494204209,773089018

%N a(n) is the smallest number k such that A358351(k) = n.

%H Rémy Sigrist, <a href="/A358352/a358352.txt">C program</a>

%e 19+sod(19)+pod(19) = 24+sod(24)+pod(24) = 31+sod(31)+pod(31) = 38, and there is no integer < 38 for which function A161351 has 3 preimages, so a(3) = 38.

%t f[n_] := n + Total[(d = IntegerDigits[n])] + Times @@ d; s = With[{m = 10^7}, BinCounts[Table[f[n], {n, 1, m}], {1, m, 1}]]; FirstPosition[s, #] & /@ Range[0, Max[s]] // Flatten (* _Amiram Eldar_, Nov 19 2022 *)

%o (PARI) first(n) = my(res = vector(n)); for(i = 1, n, c = i + sumdigits(i) + vecprod(digits(i)); if(c <= n, res[c]++ ) ); res; \\ A358351

%o lista(nn) = my(v=first(nn)); for (n=0, 20, my(vs = select(x->(x==n), v, 1)); if (#vs, print1(vs[1], ", "), break);); \\ _Michel Marcus_, Nov 20 2022

%o (C) See Links section.

%Y Cf. A006064, A007953, A007954, A161351, A358350, A358351.

%K nonn,base,more

%O 0,2

%A _Bernard Schott_, Nov 19 2022

%E a(4)-a(5) from _Michel Marcus_, Nov 19 2022

%E a(6)-a(9) from _Amiram Eldar_, Nov 19 2022

%E a(10)-a(11) from _Rémy Sigrist_, Nov 20 2022