A010349 Base-7 Armstrong or narcissistic numbers, written in base 7.

1, 2, 3, 4, 5, 6, 13, 34, 44, 63, 250, 251, 305, 505, 12205, 12252, 13350, 13351, 15124, 36034, 205145, 1424553, 1433554, 3126542, 4355653, 6515652, 125543055, 161340144, 254603255, 336133614, 542662326, 565264226, 13210652042, 13213641035, 13261421245, 23662020022, 52112660266

Offset

1,2

Comments

From M. F. Hasler, Nov 20 2019: (Start)

Like the other single-digit terms, zero would satisfy the definition (n = Sum_{i=1..k} d[i]^k where d[1..k] are the base 7 digits of n), but here only positive numbers are considered.

Whenever a(n) ends in zero (n = 11, 17, 22, 38, 57), then a(n+1) = a(n) + 1 is also a solution to the above equation. (End)

Links

Joseph Myers, Table of n, a(n) for n = 1..59 (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.

Prog

(PARI) [fromdigits(digits(n, 7))|n<-A010350] \\ M. F. Hasler, Nov 18 2019

Crossrefs

Cf. A010350 (a(n) written in base 10).

In other bases: A010343 (base 4), A010345 (base 5), A010347 (base 6), A010351 (base 8), A010352 (base 9), A005188 (base 10).

Sequence in context: A259541 A274838 A200331 * A032995 A046063 A065638

Adjacent sequences: A010346 A010347 A010348 * A010350 A010351 A010352

Keyword

base,fini,full,nonn

Author

N. J. A. Sloane

Extensions

Edited by Joseph Myers, Jun 28 2009

Status

approved