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%I #20 Aug 14 2017 03:25:40
%S 1,2,3,4,5,6,7,8,9,22,12221,13131,21212,31113,1111441111,1114114111,
%T 1141111411,1411111141,4111111114,11112421111,11121412111,11211411211,
%U 12111411121,21111411112,111122221111,111212212111,111221122111,112112211211,112121121211
%N Palindromes such that sum of digits equals product of digits.
%C Inspired by A272436.
%C Intersection of A002113 and A034710.
%C This sequence is obviously infinite.
%H Chai Wah Wu, <a href="/A272814/b272814.txt">Table of n, a(n) for n = 1..10000</a>
%t m[w_] := Flatten@Table[i, {i, 9}, {w[[i]]}]; palQ[n_] := n == FromDigits@ Reverse@ IntegerDigits@n; all[upd_] := Union@ Flatten@ Table[ FromDigits /@ Flatten[ Permutations /@ m /@ Select[ Flatten[Permutations /@ (IntegerPartitions[d + 9, {9}, Range[d+1]] -1), 1], Times @@ (Range[9]^#) == Total[# Range[9]] &], 1], {d, upd}]; Select[all@13, palQ] (* _Giovanni Resta_, May 06 2016 *)
%o (PARI) isok(n) = { my(d = digits(n)); (vecsum(d) == prod(k=1, #d, d[k])) && (subst(Polrev(d), x, 10) == n);} \\ _Michel Marcus_, May 07 2016
%Y Cf. A002113, A034710, A272436.
%K nonn,base
%O 1,2
%A _Altug Alkan_, May 06 2016
%E a(15)-a(29) from _Giovanni Resta_, May 06 2016