

A010352


Base9 Armstrong or narcissistic numbers, written in base 9.


8



1, 2, 3, 4, 5, 6, 7, 8, 45, 55, 150, 151, 570, 571, 2446, 12036, 12336, 14462, 2225764, 6275850, 6275851, 12742452, 356614800, 356614801, 1033366170, 1033366171, 1455770342, 8463825582, 131057577510, 131057577511
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OFFSET

1,2


COMMENTS

From M. F. Hasler, Nov 18 2019: (Start)
Like the other singledigit terms, zero would satisfy the definition (n = Sum_{i=1..k} d[i]^k when d[1..k] are the base9 digits of n), but here only positive numbers are considered.
Terms a(n+1) = a(n) + 1 (n = 11, 13, 20, 23, 25, 29, 33, 48, 51, 57) correspond to solutions a(n) that are multiples of 9, in which case a(n) + 1 is also a solution. (End)


LINKS

Joseph Myers, Table of n, a(n) for n = 1..58 (the full list of terms, from Winter)
Gordon L. Miller and Mary T. Whalen, Armstrong Numbers: 153 = 1^3 + 5^3 + 3^3, Fibonacci Quarterly, 303 (1992), 221224.
Eric Weisstein's World of Mathematics, Narcissistic Number
D. T. Winter, Table of Armstrong Numbers (latest backup on web.archive.org from Jan. 2010; page no longer available), published not later than Aug. 2003.


EXAMPLE

126 = 150_9 (= 1*9^2 + 5*9^1 + 0*9^0) = 1^3 + 5^3 + 0^3. It is easy to see that 126 + 1 then also satisfies this relation, as for all other terms that are multiples of 9.  M. F. Hasler, Nov 21 2019


PROG

(PARI) [fromdigits(digits(n, 9))n<A010353] \\ M. F. Hasler, Nov 18 2019


CROSSREFS

Cf. A010353 (a(n) written in base 10).
In other bases: A010343 (base 4), A010345 (base 5), A010347 (base 6), A010349 (base 7), A010351 (base 8), A005188 (base 10).
Sequence in context: A183531 A024652 A010353 * A024653 A024654 A004859
Adjacent sequences: A010349 A010350 A010351 * A010353 A010354 A010355


KEYWORD

base,fini,full,nonn


AUTHOR

N. J. A. Sloane


EXTENSIONS

Edited by Joseph Myers, Jun 28 2009


STATUS

approved



