A309787 Palindromes whose product of digits are palindromes with at least two digits.

676, 777, 16761, 17771, 23732, 32723, 61716, 71717, 1167611, 1177711, 1237321, 1327231, 1617161, 1717171, 2137312, 2317132, 3127213, 3217123, 6117116, 7117117, 111676111, 111777111, 112373211, 113272311, 116171611, 117171711, 121373121, 123171321

Offset

1,1

Comments

For n < 40 every term relates to 676 or 777.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10912

Example

For 676: 6*7*6 = 252.
For 1717171: 1*7*1*7*1*7*1 = 343.

Maple

ispali:= proc(n) option remember; local L, i;
L:= convert(n, base, 10);
andmap(i -> L[i]=L[-i], [$1..floor(nops(L)/2)])
end proc:
P[1]:= [$1..9]:
P[2]:= [seq(11*i, i=1..9)]:
for d from 3 to 13 do
  P[d]:= [seq(seq((10^(d-1)+1)*i+10*x, x=P[d-2]), i=1..9)]
od:
filter:= proc(n) local p; p:= convert(convert(n, base, 10), `*`);
  p >= 11 and ispali(p)
end proc:
map(op, [seq(select(filter, P[d]), d=1..13)]); # Robert Israel, Nov 14 2019

Mathematica

pd[n_] := Times @@ IntegerDigits[n]; aQ[n_] := PalindromeQ[n] && (p = pd[n]) > 9 && PalindromeQ[p]; Select[Range[10^7], aQ] (* Amiram Eldar, Nov 12 2019 *)

Prog

(Magma) f:=func<n|Intseq(n) eq Reverse(Intseq(n))>; g:=func<m| #Intseq(&*Intseq(m)) ge 2>; [k:k in [1..10000000]| f(k) and f(&*Intseq(k)) and g(k)]; // Marius A. Burtea, Nov 12 2019

Crossrefs

Cf. A002113, A117055

Sequence in context: A358174 A173134 A258963 * A064963 A300984 A185794

Adjacent sequences: A309784 A309785 A309786 * A309788 A309789 A309790

Keyword

nonn,base

Author

Maxim Veselov, Nov 11 2019

Extensions

Corrected by Robert Israel, Nov 14 2019

Status

approved