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
Examples
99999999 * 100000003 = 100000001//99999997, where // denotes concatenation.
Links
- Chai Wah Wu, Table of n, a(n) for n = 1..121
Programs
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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