A244541 -id:A244541 - cp's OEIS frontend

A244547 Numbers k with nonzero digits such that k +/- the product of digits of k are both palindromes.

1, 2, 3, 4, 247, 252, 348, 843, 15451, 25152, 25252, 25352, 25452, 36563, 36968, 44594, 51165, 51415, 52125, 52225, 52325, 52425, 63536, 92529, 1455541, 1545451, 1595451, 1954591, 2255522, 2524752, 2525252, 2534852, 2584352, 2853582, 2856582, 3159563, 3354533, 3524753, 3534353

Offset: 1

Derek Orr, Jun 29 2014

			247 has all digits > 0. 247 - 2*4*7 = 191 is a palindrome, and 247 + 2*4*7 = 303 is a palindrome. Thus 247 is a member of this sequence.

Cf. A244541, A007954.

Cf. A002113, A052382.

Select[Range@100000,(p=#+{1,-1}*Times@@IntegerDigits@#; Differences@p!={0}&&AllTrue[p,PalindromeQ])&] (* Hans Rudolf Widmer, Sep 03 2023 *)

rev(n)={r="";for(i=1,#digits(n),r=concat(Str(digits(n)[i]),r));return(eval(r))}
for(n=1,10^7,dig=digits(n);p=prod(k=1,#dig,dig[k]);if(p!=0,mi=n-p;ma=n+p;if(rev(mi)==mi&&rev(ma)==ma,print1(n,", "))))

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

Original entry on oeis.org

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

Derek Orr, Jun 29 2014

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

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

Cf. A007954, A244541.

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

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,", "))))

cp's OEIS Frontend

A244547 Numbers k with nonzero digits such that k +/- the product of digits of k are both palindromes.

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