A309787 - OEIS

%I #63 Sep 08 2022 08:46:22

%S 676,777,16761,17771,23732,32723,61716,71717,1167611,1177711,1237321,

%T 1327231,1617161,1717171,2137312,2317132,3127213,3217123,6117116,

%U 7117117,111676111,111777111,112373211,113272311,116171611,117171711,121373121,123171321

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

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

%H Chai Wah Wu, <a href="/A309787/b309787.txt">Table of n, a(n) for n = 1..10912</a>

%e For 676: 6*7*6 = 252.

%e For 1717171: 1*7*1*7*1*7*1 = 343.

%p ispali:= proc(n) option remember; local L,i;

%p L:= convert(n,base,10);

%p andmap(i -> L[i]=L[-i], [$1..floor(nops(L)/2)])

%p end proc:

%p P[1]:= [$1..9]:

%p P[2]:= [seq(11*i,i=1..9)]:

%p for d from 3 to 13 do

%p   P[d]:= [seq(seq((10^(d-1)+1)*i+10*x, x=P[d-2]),i=1..9)]

%p od:

%p filter:= proc(n) local p; p:= convert(convert(n,base,10),`*`);

%p   p >= 11 and ispali(p)

%p end proc:

%p map(op,[seq(select(filter, P[d]),d=1..13)]); # _Robert Israel_, Nov 14 2019

%t 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 *)

%o (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

%Y Cf. A002113, A117055

%K nonn,base

%O 1,1

%A _Maxim Veselov_, Nov 11 2019

%E Corrected by _Robert Israel_, Nov 14 2019