A116210 Numbers k such that k concatenated with k+7 gives the product of two numbers which differ by 8.

73, 101, 466, 577, 913, 938, 1027699544347561123497066503878337002, 1043891904746431592729642732987859418, 1406975496023772119400647610836667853, 3905041089422306453928649115284570106, 4582028691256280367677282506239892877, 4616148891509946292221374856300250093

Offset

1,1

Links

Table of n, a(n) for n=1..12.

Example

938//945 = 965 * 973, where // denotes concatenation.

Prog

(Python)
from itertools import count, islice
from sympy import sqrt_mod
def A116210_gen(): # generator of terms
    for j in count(0):
        b = 10**j
        a = b*10+1
        for k in sorted(sqrt_mod(23, a, all_roots=True)):
            if a*(b-7) <= k**2-23 < a*(a-8) and k>4:
                yield (k**2-23)//a
A116210_list = list(islice(A116210_gen(), 10)) # Chai Wah Wu, Feb 22 2024

Crossrefs

Cf. A116202, A116209, A116211, A116223, A116341.

Sequence in context: A139990 A327714 A179154 * A180522 A238679 A157120

Adjacent sequences: A116207 A116208 A116209 * A116211 A116212 A116213

Keyword

nonn,base

Author

Giovanni Resta, Feb 06 2006

Extensions

a(10)-a(12) from Chai Wah Wu, Feb 22 2024

Status

approved