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A368062 Numbers k such that k = A257850(k) + A257297(k).

%I A368062 #108 Dec 19 2024 11:46:20
%S A368062 0,36,655,1258,6208,12508,45715,65455,75385,125008,235297,1250008,
%T A368062 2857144,3214288,4210528,6545455,6792453,12500008,34615386,47058824,
%U A368062 87671233,125000008,654545455,1250000008,9529411765,12500000008,39130434783,45714285715,65454545455,75384615385
%N A368062 Numbers k such that k = A257850(k) + A257297(k).
%H A368062 Kevin Ryde, <a href="/A368062/b368062.txt">Table of n, a(n) for n = 1..700</a>
%H A368062 Nicolas Bělohoubek, <a href="/A368062/a368062_1.txt">C# program</a>
%H A368062 Nicolas Bělohoubek, <a href="/A368062/a368062_4.txt">Subsequences of form A-(B)-C</a>
%H A368062 Kevin Ryde, <a href="/A368062/a368062.gp.txt">PARI/GP Code</a>
%e A368062      0 = 0*0   +   0*0;
%e A368062     36 = 3*6   +   3*6;
%e A368062    655 = 6*55  +  65*5;
%e A368062   6208 = 6*208 + 620*8;
%e A368062   ...
%t A368062 Select[Range[0,10^6], Part[digits=IntegerDigits[#],1]FromDigits[Drop[digits,1]] + FromDigits[Drop[digits,-1]]Part[digits,Length[digits]] == # &] (* _Stefano Spezia_, Dec 10 2023 *)
%o A368062 (Python)
%o A368062 def ok(n):
%o A368062     if n < 10: return n == 0
%o A368062     s = str(n)
%o A368062     return n == int(s[0])*int(s[1:]) + (n%10)*(n//10)
%o A368062 print([k for k in range(10**6) if ok(k)]) # _Michael S. Branicky_, Dec 10 2023
%o A368062 (Python) # faster for generating initial segment of sequence
%o A368062 from itertools import count, islice
%o A368062 def agen(): # generator of terms
%o A368062     yield 0
%o A368062     for digits in count(2):
%o A368062         for first in range(1, 10):
%o A368062             base = first*10**(digits-1)
%o A368062             for rest in range(10**(digits-1)):
%o A368062                 n = base + rest
%o A368062                 if first*rest + (n%10)*(n//10) == n:
%o A368062                     yield n
%o A368062             print("...", digits, first, time()-time0, alst)
%o A368062 print(list(islice(agen(), 18))) # _Michael S. Branicky_, Dec 10 2023
%o A368062 (PARI) \\ See links.
%Y A368062 Cf. A257850, A257297.
%K A368062 nonn,base
%O A368062 1,2
%A A368062 _Nicolas Bělohoubek_, Dec 10 2023
%E A368062 a(24)-a(30) from _Michael S. Branicky_, Dec 10 2023