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%I #38 Sep 12 2023 20:46:36
%S 0,655,1461,1642,2361,3442,6550,14610,16420,23610,34420,65500,146100,
%T 164200,236100,344200,655000,1461000,1642000,2361000,3442000,6550000,
%U 14610000,16420000,23610000,34420000,65500000,146100000,164200000,236100000,344200000
%N 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 L-i digits, for i from 1 to L-1, e.g., f(1234) = 1*234 + 12*34 + 123*4 = 1134. Sequence gives k such that f(k) = k.
%C Are there any terms > 3442 that are not just a previous term followed by zeros?
%C Concerning this question, see the a-file with terms up to 10^6 expressed in the corresponding base for similar sequences in base 2 to 37. - _Michel Marcus_, Dec 17 2015
%H Sean A. Irvine, <a href="/A065759/b065759.txt">Table of n, a(n) for n = 1..47</a>
%H Michel Marcus, <a href="/A065759/a065759.txt">Similar sequences in base b=2 to 37</a>
%F Conjectures from _Colin Barker_, Jun 18 2019: (Start)
%F G.f.: x*(655 + 1461*x + 1642*x^2 + 2361*x^3 + 3442*x^4) / (1 - 10*x^5).
%F a(n) = 10*a(n-5) for n>5.
%F (End)
%e n = 655 is in the sequence because f(655) = 6*55 + 65*5 = 330 + 325 = 655.
%t 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 *)
%o (PARI) isok(n) = n == sum(k=1, #Str(n), (n\10^k)*(n % 10^k)); \\ _Michel Marcus_, Dec 16 2015
%K base,nonn
%O 1,2
%A Jonathan Ayres (jonathan.ayres(AT)btinternet.com), Nov 17 2001
%E 0 added by _Rémy Sigrist_, May 21 2021
%E More terms from _Sean A. Irvine_, Sep 12 2023
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