Review: A069554

[David Wilson]

I need some help with this sequence; read on.

The current name of A069554 is:

%N A069554 Smallest number k such that (k, R(k))= n, where R(k) is the digit
reversal of n. a(n) is 0 for a multiple of 10.

I suggest that we change this to:

%N A069554 Smallest k > 0 with gcd(k, rev(k)) = n, where rev(k) is digit
reversal of k, or 0 if no such k exists.

I suggest the change because (1) I consider the notation gcd(a, b)
preferable to the ambiguous (a, b),
and (2) I suspect there exist n other than multiples of 10 for which no k
exists; see below.

Given my modified description, my proposed correction/extension is:

%N A069554
1,2,3,4,5,6,7,8,9,0,11,48,1495,2072,510,2192,1156,234,2489,0,168,22,
%N A069554
3358,840,5200,2678,2889,4256,5017,0,1178,21920,33,20774,5075,216,0,
%N A069554
2318,1677,0,1066,2436,15523,44,540,20516,30644,8400,18718,0,1479,21788

The corrections are:

a(17) changed from 1207 to 1156.
a(24) changed from 2136 to 840.  a(15) = 510 shows that numbers ending in 0
are acceptable.

The questionable elements are:

a(37) = 0.  Empirical evidence indicates that 37 | gcf(k, rev(k)) ==> 111 |
gcf(k, rev(k)),
in which case gcf(k, rev(k)) = 37 has no solution.  If true, I imagine it is
a trivial exercise
in modular arithmetic, but I am not presently up to the task. Any help from
an SF would
be appreciated.  Lacking this proof, a(37) is conjectural.