A334661 Numbers k such that k*sod(k) and k+sod(k) are both palindromes, where sod(k) denotes the sum of digits of k (A007953).

0, 1, 2, 3, 124, 829, 186373637, 186454637, 187272737, 195454547, 23212121199, 23302120299, 1230303030288, 1312121212098, 1320303030198, 1321121211198, 1321203021198, 1321211121198, 1330121210298, 1330203020298, 1330211120298, 1330301030298, 2130303030279

Offset

1,3

Comments

For the first 2729 terms, most of them have digit sum 33. The only terms a(n) for n <= 2729 for which the digit sum is not 33 are for n = 1,...,10, 716, 2194, 2195. - Chai Wah Wu, May 15 2020

Links

Chai Wah Wu, Table of n, a(n) for n = 1..2729

Example

The sum of digits of 829 is 19 and 829*19 = 15751 and 829+19 = 848 are palindromes, so 829 is a term.

Mathematica

Select[Range[0, 999], (s = Plus @@ IntegerDigits[#]; PalindromeQ[# s] && PalindromeQ[# + s]) &]

Prog

(PARI) ispal(n) = my(d=digits(n)); d == Vecrev(d);
isok(m) = my(s=sumdigits(m)); ispal(m*s) && ispal(m+s); \\ Michel Marcus, May 08 2020

Crossrefs

Intersection of A229549 and A229545.

Cf. A007953, A334533.

Sequence in context: A065841 A051177 A371271 * A258968 A125674 A180533

Adjacent sequences: A334658 A334659 A334660 * A334662 A334663 A334664

Keyword

nonn,base

Author

Giovanni Resta, May 07 2020

Status

approved