A116260 n times n+4 gives the concatenation of two numbers m and m-4.

9, 99, 999, 9999, 99999, 999999, 9999999, 99999999, 999999999, 9999999999, 36363636362, 45454545453, 54545454544, 63636363635, 72727272726, 81818181817, 90909090908, 99999999999, 999999999999, 9999999999999

Offset: 1

Author

Giovanni Resta, Feb 06 2006

Keywords

• nonn
• base

Examples

			99999999 * 100000003 = 100000001//99999997, where // denotes concatenation.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..121

Crossrefs

Cf. A116129, A116254, A116259, A116261, A116267.

Programs

Python

from itertools import count, islice
from sympy import sqrt_mod
def A116260_gen(): # generator of terms
    for j in count(0):
        b = 10**j
        a = b*10+1
        for k in sorted(sqrt_mod(0,a,all_roots=True))+[a]:
            if a*(b+4) <= k**2 < a*(a+3):
                yield k-2
A116260_list = list(islice(A116260_gen(),20)) # Chai Wah Wu, Feb 19 2024

Formula

10^d-1 for d>0 are terms. - Chai Wah Wu, Feb 19 2024