A035027 Greatest integer that is <= the sum of the n-th powers of its digits.

9, 99, 1999, 19999, 229999, 2999999, 29999999, 299999999, 2999999999, 30999999999, 309999999999, 3099999999999, 29999999999999, 299999999999999, 2999999999999999, 26999999999999999, 259999999999999999

Offset

1,1

Comments

If we suppress trailing 9's, we get the strings 0, 0, 1, 1, 22, 2, 2, 2, 2, 30, 30, 30, 2, 2, 2, 26, 25, 24, 23, 22, 20, 1, 1, 17, 17, 15, 14, 13, 12, 11, 10, 102, 0, 090, 081, 075, 06, 064, 05, 055 for n up to 40; also (as correctly reported by Stewart) 000251 for a(100). Here one should pad with 9's until obtaining exactly n+1 digits. This sequence of digit strings cannot be conveniently represented in the OEIS because the number of leading 0's is significant! - Don Knuth, Sep 07 2015

Links

Table of n, a(n) for n=1..17.

B. M. Stewart, Sums of functions of digits, Canad. J. Math., 12 (1960), 374-389. - Don Knuth, Sep 07 2015

Example

2^5 + 2^5 + 9^5 + 9^5 + 9^5 + 9^5 >= 229999 but "<" for all greater integers, so a(5) = 229999.
Stewart, in his Table VI, incorrectly stated that a(5)=299999. - Don Knuth, Sep 07 2015

Crossrefs

Sequence in context: A113395 A070068 A068668 * A196487 A262540 A265203

Adjacent sequences: A035024 A035025 A035026 * A035028 A035029 A035030

Keyword

base,nonn,nice

Author

Ulrich Schimke (ulrschimke(AT)aol.com)

Extensions

More terms from Naohiro Nomoto, Jul 29 2001

Status

approved