

A010353


Base9 Armstrong or narcissistic numbers (written in base 10).


14



1, 2, 3, 4, 5, 6, 7, 8, 41, 50, 126, 127, 468, 469, 1824, 8052, 8295, 9857, 1198372, 3357009, 3357010, 6287267, 156608073, 156608074, 403584750, 403584751, 586638974, 3302332571, 42256814922, 42256814923, 114842637961, 155896317510, 552468844242, 552468844243, 647871937482, 686031429775
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OFFSET

1,2


COMMENTS

From M. F. Hasler, Nov 20 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 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)


LINKS

Joseph Myers, Table of n, a(n) for n = 1..58 (the full list of terms, from Winter)
Eric Weisstein's World of Mathematics, Narcissistic Number
D. T. Winter, Table of Armstrong Numbers


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 20 2019


PROG

(PARI) select( {is_A010353(n)=n==vecsum([d^#nd<n=digits(n, 9)])}, [0..10^4]) \\ This gives only terms < 10^6, for illustration of is_A010353().  M. F. Hasler, Nov 20 2019


CROSSREFS

Cf. A010352 (a(n) written in base 9).
In other bases: A010344 (base 4), A010346 (base 5), A010348 (base 6), A010350 (base 7), A010354 (base 8), A005188 (base 10), A161948 (base 11), A161949 (base 12), A161950 (base 13), A161951 (base 14), A161952 (base 15), A161953 (base 16).
Sequence in context: A004848 A183531 A024652 * A010352 A024653 A024654
Adjacent sequences: A010350 A010351 A010352 * A010354 A010355 A010356


KEYWORD

base,fini,full,nonn


AUTHOR

N. J. A. Sloane


EXTENSIONS

Edited by Joseph Myers, Jun 28 2009


STATUS

approved



