A010352 Base-9 Armstrong or narcissistic numbers, written in base 9.

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• base
• fini
• full
• nonn

Comments

From M. F. Hasler, Nov 18 2019: (Start)

Like the other single-digit terms, zero would satisfy the definition (n = Sum_{i=1..k} d[i]^k when d[1..k] are the base-9 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)

Examples

			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
		

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, 30-3 (1992), 221-224.
• 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.

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).

Programs

PARI

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

Extensions

Edited by Joseph Myers, Jun 28 2009