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

Author

Giovanni Resta, Feb 06 2006

Keywords

• nonn
• base

Examples

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

Links

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

Crossrefs

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

Programs

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

Extensions

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