A357678 Numbers k equal to the integer log of the sum of k and its digit reversal.

8, 17, 107

Offset

1,1

Comments

10^n + 7 is a term if 10^n + 1 is prime, however that is conjectured to occur only for n = 0, 1 and 2.

It can be shown that all terms have form 10^n + 7. Hence, terms from a(2) onward correspond to generalized Fermat primes base 10; i.e., primes in A080176. - Max Alekseyev, Nov 01 2025

Links

Table of n, a(n) for n=1..3.

Example

a(3) = 107 is a term because the integer log of (107 + 701 = 808 = 2^3*101) is 3*2 + 101 = 107.

Maple

rev:= proc(n) local L, i; L:= convert(n, base, 10): add(L[-i]*10^(i-1), i=1..nops(L)) end proc:
filter:= proc(n) local s, t;
   s:= n + rev(n);
   n = add(t[1]*t[2], t=ifactors(s)[2])
end proc:
select(filter, [$1..10^6]);

Crossrefs

Cf. A001414, A004086, A056964, A080176.

Sequence in context: A350683 A177129 A177178 * A097405 A192282 A088588

Adjacent sequences: A357675 A357676 A357677 * A357679 A357680 A357681

Keyword

nonn,base,bref,more,hard

Author

J. M. Bergot and Robert Israel, Oct 08 2022

Status

approved