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A272814 Palindromes such that sum of digits equals product of digits. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 11 22:17 EDT 2021. Contains 342895 sequences. (Running on oeis4.)