A244542 Palindromes n such that n +/- the product of digits of n are both palindromes.

1, 2, 3, 4, 101, 202, 252, 303, 404, 505, 606, 707, 808, 909, 1001, 2002, 3003, 4004, 5005, 6006, 7007, 8008, 9009, 10001, 10101, 10201, 10301, 10401, 10501, 10601, 10701, 10801, 10901, 11011, 12021, 13031, 14041, 15051, 15451, 16061, 17071, 18081, 19091, 20002, 20102, 20202

Offset: 1

Author

Derek Orr, Jun 29 2014

Keywords

• nonn
• base

Comments

These are the palindromes in A244541.

All palindromes with a zero will be in this sequence.

The palindromes that do not contain a zero but do satisfy the definition begin 1, 2, 3, 4, 252, 15451, 25152, 25252, 25352, 25452, 36563, 51415, 52125, 52225, 52325, 52425, 63536, 92529, 1455541, 1545451, 1954591 . . . - Harvey P. Dale, May 14 2019

Examples

			101 - 1*0*1 and 101 + 1*0*1 are both palindromes (still 101). So 101 is a member of this sequence.
		

Crossrefs

Cf. A007954, A244541.

Programs

Mathematica

Select[Range[30000],AllTrue[#+{0,Times@@IntegerDigits[#],-Times@@IntegerDigits[#]},PalindromeQ]&] (* Harvey P. Dale, Aug 14 2025 *)

PARI

rev(n)={r="";for(i=1,#digits(n),r=concat(Str(digits(n)[i]),r));return(eval(r))}
for(n=1,10^5,if(rev(n)==n,dig=digits(n);p=prod(k=1,#dig,dig[k]);mi=n-p;ma=n+p;if(rev(mi)==mi&&rev(ma)==ma,print1(n,", "))))