

A010354


Base8 Armstrong or narcissistic numbers (written in base 10).


16



1, 2, 3, 4, 5, 6, 7, 20, 52, 92, 133, 307, 432, 433, 16819, 17864, 17865, 24583, 25639, 212419, 906298, 906426, 938811, 1122179, 2087646, 3821955, 13606405, 40695508, 423056951, 637339524, 6710775966, 13892162580, 32298119799, 97095152738, 98250308556, 98317417420, 125586038802
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OFFSET

1,2


COMMENTS

Like the other singledigit terms, zero would satisfy the definition (n = Sum_{i=1..k} d[i]^k when d[1..k] are the base 8 digits of n), but here only positive numbers are considered.  M. F. Hasler, Nov 20 2019


LINKS

Joseph Myers, Table of n, a(n) for n = 1..62 (the full list of terms, from Winter)
Eric Weisstein's World of Mathematics, Narcissistic Number
D. T. Winter, Table of Armstrong Numbers


EXAMPLE

From M. F. Hasler, Nov 20 2019: (Start)
20 = 24_8 (in base 8), and 2^2 + 4^2 = 20.
432 = 660_8, and 6^3 + 6^3 + 0^3 = 432; it's easy to see that 432 + 1 then also satisfies the equation, as for any term that is a multiple of 8. (End)


PROG

(PARI) select( {is_A010354(n)=n==vecsum([d^#nd<n=digits(n, 8)])}, [0..10^6]) \\ This gives only terms < 10^6, for illustration of is_A010354().  M. F. Hasler, Nov 20 2019


CROSSREFS

Cf. A010351 (a(n) written in base 8).
In other bases: A010344 (base 4), A010346 (base 5), A010348 (base 6), A010350 (base 7), A010353 (base 9), A005188 (base 10), A161948 (base 11), A161949 (base 12), A161950 (base 13), A161951 (base 14), A161952 (base 15), A161953 (base 16).
Sequence in context: A200333 A024644 A297182 * A070759 A282138 A106275
Adjacent sequences: A010351 A010352 A010353 * A010355 A010356 A010357


KEYWORD

base,fini,full,nonn


AUTHOR

N. J. A. Sloane


EXTENSIONS

Edited by Joseph Myers, Jun 28 2009


STATUS

approved



