A116275 Numbers k such that k*(k+4) gives the concatenation of two numbers m and m-2.

8872, 9009, 83352840, 99000099, 329767122286, 670232877711, 738226276371, 933006600339, 999000000999, 3779410975143113, 3872816717528065, 4250291784692548, 4278630943941865, 4372036686326817, 4749511753491300, 5250488246508697, 5627963313673180, 5721369056058132

Offset

1,1

Links

Chai Wah Wu, Table of n, a(n) for n = 1..1187

Example

99000099 * 99000103 = 98010199//98010197, where // denotes concatenation.

Prog

(Python)
from itertools import count, islice
from sympy import sqrt_mod
def A116275_gen(): # generator of terms
    for j in count(0):
        b = 10**j
        a = b*10+1
        for k in sorted(sqrt_mod(2, a, all_roots=True)):
            if a*(b+3) <= k**2-2 < a*(a+2):
                yield k-2
A116275_list = list(islice(A116275_gen(), 30)) # Chai Wah Wu, Feb 19 2024

Crossrefs

Cf. A115426, A116267, A116274, A116276, A116288.

Sequence in context: A031625 A046506 A116242 * A116295 A115427 A236614

Adjacent sequences: A116272 A116273 A116274 * A116276 A116277 A116278

Keyword

nonn,base

Author

Giovanni Resta, Feb 06 2006

Extensions

a(16)-a(18) from Chai Wah Wu, Feb 19 2024

Status

approved