

A230638


Smallest number m such that u + (sum of base4 digits of u) = m has exactly n solutions.


19




OFFSET

1,2


COMMENTS

Indices of records in A230632: a(n) is the index of the first n in A230632.
The terms are a(1)=0, a(2)=4^2+1, a(3)=4^7+1, a(4)=4^12+17+1, a(5)=4^5368+17+1, a(6)=4^10924+16385+1, a(7)=4^5597880+16385+20. Note that a(7) breaks the pattern of the first six terms.
a(8) = 4^16777229 + 4^12 + 19.
For the leading power of 4 see A230637.


LINKS

Table of n, a(n) for n=1..4.
Max Alekseyev, Table of expressions for a(n), for n=1..100
Max A. Alekseyev and N. J. A. Sloane, On Kaprekar's Junction Numbers, arXiv:2112.14365, 2021; Journal of Combinatorics and Number Theory, 2022 (to appear).
Index entries for Colombian or self numbers and related sequences


EXAMPLE

n=2: the two solutions to u+(base4 digitsum of u) = 17 are 13 and 16.
n=3: the three solutions to u+(base4 digitsum of u) = 4^7+1 are 4^7, 4^715, 4^718.
n=4: the four solutions to u+(base4 digitsum of u) = 4^12+17+1 are 4^12+{16, 13, 14, 17}.


CROSSREFS

Cf. A230637.
Related base4 sequences: A053737, A230631, A230632, A010064, A230633, A230634, A230635, A230636, A230637, A230638, A010065 (trajectory of 1)
Smallest number m such that u + (sum of baseb digits of u) = m has exactly n solutions, for bases 2 through 10: A230303, A230640, A230638, A230867, A238840, A238841, A238842, A238843, A006064.
Sequence in context: A300596 A308962 A191964 * A308671 A308670 A308571
Adjacent sequences: A230635 A230636 A230637 * A230639 A230640 A230641


KEYWORD

nonn,base


AUTHOR

N. J. A. Sloane, Oct 31 2013


EXTENSIONS

a(8) from Max Alekseyev, Oct 31 2013


STATUS

approved



