A117055 -id:A117055 - cp's OEIS frontend

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

Maxim Veselov, Nov 11 2019

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

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

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

Cf. A002113, A117055

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

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

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 *)

Corrected by Robert Israel, Nov 14 2019

A082207 Palindromes whose product of digits is a positive palindrome.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 111, 121, 131, 141, 151, 161, 171, 181, 191, 212, 222, 313, 676, 777, 1111, 1221, 1331, 2112, 3113, 11111, 11211, 11311, 11411, 11511, 11611, 11711, 11811, 11911, 12121, 12221, 13131, 16761, 17771, 21112, 21212

Offset: 1

Amarnath Murthy, Apr 10 2003

The unary sequence A000042 is a trivial subsequence.
Conjecture: There are infinitely many terms in the sequence (of the type 777) for which the product of digits > 10.
Subset of A117055, containing terms for which product of digits is greater than 0. - Jayanta Basu, May 15 2013

			777 is a term as 7^3 = 343 is a palindrome.

Harvey P. Dale, Table of n, a(n) for n = 1..89 (all terms up to 10 million)

Cf. A082208.

id[n_]:=IntegerDigits[n]; palQ[n_]:=Reverse[x=id[n]]==x; t={}; Do[If[palQ[n] && (y=Times@@id[n]) > 0 && palQ[y], AppendTo[t,n]], {n,21220}]; t (* Jayanta Basu, May 15 2013 *)
Select[Range[22000],FreeQ[IntegerDigits[#],0]&&AllTrue[{#,Times @@ IntegerDigits[ #]},PalindromeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Nov 22 2019 *)

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 19 2003

cp's OEIS Frontend

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

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