OFFSET
1,2
COMMENTS
Integers with at least one 0 digit cannot be terms. There is no other palindrome after 999999999, but is the sequence complete? The non-palindromic numbers in the sequence are 864, 362436, 18181818, 26666664, 36484836, 48363648 and 1666516665, in which zero, seven and nine do not appear as a digit. These non-palindromes are multiples of 3 and have a multiple of 6 as the sum of their digits.
The sequence is finite because the sum of the reciprocals of the digits of every zeroless number greater than 10^81-1 exceeds 9, while the ratio R(n)/n is always smaller than 9. a(43) > 10^13, if it exists. - Giovanni Resta, Aug 12 2019
LINKS
Stéphane Rézel, Table of n, a(n) for n = 1..42
EXAMPLE
864 is in the sequence because 864 * (1/8 + 1/6 + 1/4) = 468, the digit reversal of 864.
MATHEMATICA
Select[Range[365*10^5], #*Total[1/IntegerDigits[#]]==IntegerReverse[#]&]//Quiet (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 09 2020 *)
PROG
(PARI) isok(k) = my(d=digits(k)); if (vecmin(d), k*sum(i=1, #d, 1/d[i]) == fromdigits(Vecrev(d))); \\ Michel Marcus, Aug 11 2019
(Magma) [k:k in [1..4000000]| not 0 in Set(Intseq(k)) and k*(&+[1/Intseq(k)[i]:i in [1..#Intseq(k)]]) eq Seqint(Reverse(Intseq(k)))]; // Marius A. Burtea, Aug 11 2019
CROSSREFS
KEYWORD
nonn,base,fini
AUTHOR
Stéphane Rézel, Aug 11 2019
STATUS
approved