

A065759


For a number k of length L, let f(k) be the sum of the products of the first i digits of k multiplied by the last Li digits, for i from 1 to L1, e.g., f(1234) = 1*234 + 12*34 + 123*4 = 1134. Sequence gives k such that f(k) = k.


4



0, 655, 1461, 1642, 2361, 3442, 6550, 14610, 16420, 23610, 34420, 65500, 146100, 164200, 236100, 344200, 655000, 1461000, 1642000, 2361000, 3442000, 6550000, 14610000, 16420000, 23610000, 34420000, 65500000, 146100000, 164200000
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OFFSET

1,2


COMMENTS

Are there any terms > 3442 that are not just a previous term followed by zeros?
Concerning this question, see the afile with terms up to 10^6 expressed in the corresponding base for similar sequences in base 2 to 37.  Michel Marcus, Dec 17 2015


LINKS

Table of n, a(n) for n=1..29.
Michel Marcus, Similar sequences in base b=2 to 37


FORMULA

Conjectures from Colin Barker, Jun 18 2019: (Start)
G.f.: x*(655 + 1461*x + 1642*x^2 + 2361*x^3 + 3442*x^4) / (1  10*x^5).
a(n) = 10*a(n5) for n>5.
(End)


EXAMPLE

n = 655 is in the sequence because f(655) = 6*55 + 65*5 = 330 + 325 = 655.


MATHEMATICA

f[n_] := Block[{a = {}, e = IntegerLength@ n  1, k}, Do[AppendTo[a, #*(n  #*10^(e  k)) &@ Floor[n/10^(e  k)]], {k, 0, e  1}]; Total@ a]; Select[0, Range[10^6], f@ # == # &] (* Michael De Vlieger, Dec 18 2015 *)


PROG

(PARI) isok(n) = n == sum(k=1, #Str(n), (n\10^k)*(n % 10^k)); \\ Michel Marcus, Dec 16 2015


CROSSREFS

Sequence in context: A250701 A250158 A265737 * A280445 A220057 A194653
Adjacent sequences: A065756 A065757 A065758 * A065760 A065761 A065762


KEYWORD

base,nonn


AUTHOR

Jonathan Ayres (jonathan.ayres(AT)btinternet.com), Nov 17 2001


EXTENSIONS

0 added by Rémy Sigrist, May 21 2021


STATUS

approved



