A272814 Palindromes such that sum of digits equals product of digits.

1, 2, 3, 4, 5, 6, 7, 8, 9, 22, 12221, 13131, 21212, 31113, 1111441111, 1114114111, 1141111411, 1411111141, 4111111114, 11112421111, 11121412111, 11211411211, 12111411121, 21111411112, 111122221111, 111212212111, 111221122111, 112112211211, 112121121211

Offset

1,2

Comments

Inspired by A272436.

Intersection of A002113 and A034710.

This sequence is obviously infinite.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Mathematica

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 *)

Prog

(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

Crossrefs

Cf. A002113, A034710, A272436.

Sequence in context: A305257 A318273 A061672 * A322516 A132080 A307636

Adjacent sequences: A272811 A272812 A272813 * A272815 A272816 A272817

Keyword

nonn,base

Author

Altug Alkan, May 06 2016

Extensions

a(15)-a(29) from Giovanni Resta, May 06 2016

Status

approved