# [seqfan] is this worth to get an entry in OEIS?

Peter petsie at dordos.net
Sat Mar 20 14:18:38 CET 2010

```Dear group,

the sequence http://www.research.att.com/~njas/sequences/A099506 is
known as "a(1)=1; for n > 1, a(n)=smallest m>0 that has not appeared so
far in the sequence such that m+a(n-1) is a multiple of n.".

If the addition of m and a(n-1) is replaced by "concatenation of the
digits of a(n-1) and m (to base ten)", we get a sequence unknown to
superseeker. I attach the result of superseeker, because I'm helpless
with the equation it gives at the end of the posting"

I get as the first 100 element of my proposed sequence:
1, 2, 4, 8, 5, 10, 15, 12, 6, 20, 9, 24, 7, 14, 25, 28, 22, 32, 3, \
40, 11, 44, 16, 56, 50, 18, 36, 68, 73, 80, 29, 76, 23, 46, 55, 116, \
92, 34, 71, 60, 27, 30, 53, 108, 45, 54, 52, 128, 38, 100, 47, 84, \
111, 78, 65, 184, 110, 142, 19, 140, 91, 202, 86, 144, 95, 70, 35, \
156, 63, 210, 87, 120, 158, 138, 75, 164, 241, 176, 17, 200, 88, 150, \
147, 168, 130, 72, 21, 208, 26, 190, 281, 152, 148, 238, 165, 216, \
31, 262, 251, 300

example: a(7)=15 because a(6)=10 and 1015 is divisible by 7 (1015/7=145).

It seems that a(10^k)==(k+1)10^k. Just a coincidence?

Would you be so kind to verify these values, please?

Neil, should I supply a table with respect to the base (for example with
base 2 the first 100 values are:
1, 2, 5, 4, 11, 10, 8, 16, 7, 26, 13, 28, 27, 18, 3, 32, 15, 6, 17, \
52, 53, 20, 54, 24, 39, 78, 57, 12, 22, 62, 31, 64, 91, 58, 33, 48, \
9, 102, 63, 96, 47, 74, 37, 104, 49, 38, 59, 80, 99, 156, 75, 36, \
109, 44, 88, 152, 95, 214, 51, 72, 117, 90, 144, 128, 126, 108, 14, \
56, 77, 42, 182, 136, 112, 94, 118, 192, 205, 124, 43, 304, 179, 178, \
165, 180, 40, 166, 67, 184, 61, 134, 185, 204, 114, 238, 157, 224, \
177, 160, 349, 312

but I think it would be better to make an entry for each base separately
(?).

And is it worth it?