A082208 -id:A082208 - cp's OEIS frontend

A082207 Palindromes whose product of digits is a positive palindrome.

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

A222116 Palindromic primes whose sum of digits is also a palindromic prime.

Original entry on oeis.org

2, 3, 5, 7, 11, 101, 131, 151, 191, 313, 353, 10301, 10501, 11311, 13331, 30103, 1003001, 1123211, 1201021, 1221221, 1303031, 1311131, 3001003, 3103013, 100030001, 100050001, 100111001, 100131001, 101030101, 110111011, 110232011, 111010111, 111050111

Offset: 1

Jayanta Basu, May 13 2013

			353, a palindromic prime, is in the list since 3+5+3=11 is also a palindromic prime.

Giovanni Resta, Table of n, a(n) for n = 1..1000

Intersection of A082806 and A082208.

palQ[n_]:=FromDigits[Reverse[IntegerDigits[n]]]==n; t={}; Do[If[palQ[p=Prime[n]] && palQ[td=Total[IntegerDigits[p]]] && PrimeQ[td],AppendTo[t,p]],{n,6400000}]; t

A334249 Numbers k such that (k - digitsum(k))(k + digitsum(k)) contains k as a substring.

Original entry on oeis.org

11, 88, 101, 448, 673, 776, 1001, 2879, 3553, 9537, 10001, 14651, 36559, 49056, 51073, 54116, 59600, 100001, 505025, 998999, 1000001, 4115964, 5050250, 5133355, 10000001, 10050125, 19349727, 26550976, 33726078, 35792647, 42349456, 43605459, 50050025, 66952741, 88027284, 88819024, 100000001, 105124922

Offset: 1

Scott R. Shannon, May 05 2020

All numbers of the form 10^n + 1 (for n > 0) are in the sequence.

			11 is a term as digitsum(11) = 2 and (11 - 2)(11 + 2) = 117, which contains '11' as a substring.
9537 is a term as digitsum(9537) = 24 and (9537 - 24)(9537 + 24) = 90953793, which contains '9537' as a substring.

Giovanni Resta, Table of n, a(n) for n = 1..95

Cf. A007953, A257784, A125526, A082208, A225780.

cp's OEIS Frontend

A082207 Palindromes whose product of digits is a positive palindrome.

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A222116 Palindromic primes whose sum of digits is also a palindromic prime.

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A334249 Numbers k such that (k - digitsum(k))(k + digitsum(k)) contains k as a substring.

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