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

Author

Maxim Veselov, Nov 11 2019

Keywords

• nonn
• base

Comments

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

Examples

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

Links

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

Crossrefs

Cf. A002113, A117055

Programs

Magma

f:=func; g:=func; [k:k in [1..10000000]| f(k) and f(&*Intseq(k)) and g(k)]; // Marius A. Burtea, Nov 12 2019

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 *)

Extensions

Corrected by Robert Israel, Nov 14 2019