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

0, 36, 655, 1258, 6208, 12508, 45715, 65455, 75385, 125008, 235297, 1250008, 2857144, 3214288, 4210528, 6545455, 6792453, 12500008, 34615386, 47058824, 87671233, 125000008, 654545455, 1250000008, 9529411765, 12500000008, 39130434783, 45714285715, 65454545455, 75384615385

Offset: 1

Author

Nicolas Bělohoubek, Dec 10 2023

Keywords

• nonn
• base

Examples

			     0 = 0*0   +   0*0;
    36 = 3*6   +   3*6;
   655 = 6*55  +  65*5;
  6208 = 6*208 + 620*8;
  ...
		

Links

• Kevin Ryde, Table of n, a(n) for n = 1..700
• Nicolas Bělohoubek, C# program
• Nicolas Bělohoubek, Subsequences of form A-(B)-C
• Kevin Ryde, PARI/GP Code

Crossrefs

Cf. A257850, A257297.

Programs

Mathematica

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 *)

PARI

\\ See links.

Python

def ok(n):
    if n < 10: return n == 0
    s = str(n)
    return n == int(s[0])*int(s[1:]) + (n%10)*(n//10)
print([k for k in range(10**6) if ok(k)]) # Michael S. Branicky, Dec 10 2023

Python

# faster for generating initial segment of sequence
from itertools import count, islice
def agen(): # generator of terms
    yield 0
    for digits in count(2):
        for first in range(1, 10):
            base = first*10**(digits-1)
            for rest in range(10**(digits-1)):
                n = base + rest
                if first*rest + (n%10)*(n//10) == n:
                    yield n
            print("...", digits, first, time()-time0, alst)
print(list(islice(agen(), 18))) # Michael S. Branicky, Dec 10 2023

Extensions

a(24)-a(30) from Michael S. Branicky, Dec 10 2023