A116341 k times k+8 gives the concatenation of two numbers m and m+7.

82, 314, 679, 756, 952, 965, 3205775326418807415637845823789043451, 3230931606745075612526180113373983267, 3750967203300732832735999247776048870, 6249032796699267167264000752223951123, 6769068393254924387473819886626016726, 6794224673581192584362154176210956542

Offset: 1

Author

Giovanni Resta, Feb 06 2006

Keywords

• nonn
• base

Examples

			965 * 973 = 938//945, where // denotes concatenation, so 965 is a term.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..56

Crossrefs

Cf. A116210, A116333, A116340, A116342, A116354.

Programs

Python

from itertools import count, islice
from sympy import sqrt_mod
def A116341_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-4
A116341_list = list(islice(A116341_gen(),20)) # Chai Wah Wu, Feb 21 2024

Extensions

a(10)-a(12) from Chai Wah Wu, Feb 21 2024