login
A309787
Palindromes whose product of digits are palindromes with at least two digits.
4
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.
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
KEYWORD
nonn,base
AUTHOR
Maxim Veselov, Nov 11 2019
EXTENSIONS
Corrected by Robert Israel, Nov 14 2019
STATUS
approved