A116333 k times k+8 gives the concatenation of two numbers m and m+6.

23, 70, 480, 513, 942, 76303, 8923139715521228493004072379869, 77558981961505761619171327422086381910161500424346805, 4494071669430455134012149964165405936125116123191254722256003057119, 5505928330569544865987850035834594063874883876808745277743996942874

Offset: 1

Author

Giovanni Resta, Feb 06 2006

Keywords

• nonn
• base

Examples

			76303 * 76311 = 58227//58233, where // denotes concatenation, so 76303 is a term.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..16

Crossrefs

Cf. A116202, A116327, A116332, A116334, A116341.

Programs

Python

from itertools import count, islice
from sympy import sqrt_mod
def A116333_gen(): # generator of terms
    for j in count(0):
        b = 10**j
        a = b*10+1
        for k in sorted(sqrt_mod(22,a,all_roots=True)):
            if a*(b-6) <= k**2-22 < a*(a-7) and k>4:
                yield k-4
A116333_list = list(islice(A116333_gen(),10)) # Chai Wah Wu, Feb 21 2024

Extensions

a(8)-a(10) from Chai Wah Wu, Feb 21 2024