A116267 Numbers k such that k*(k+4) gives the concatenation of two numbers m and m-3.

8, 98, 426, 571, 725, 844, 998, 7808, 9998, 36363, 63634, 99998, 326732, 673265, 999998, 4545452, 5454545, 9999998, 47058821, 52941176, 99999998, 331983805, 332667332, 384615384, 422892896, 475524475, 524475522, 577107101, 615384613, 667332665, 668016192, 719964244

Offset: 1

Author

Giovanni Resta, Feb 06 2006

Keywords

• nonn
• base

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A116136, A116260, A116266, A116268, A116275.

Programs

Python

from itertools import count, islice
from sympy import sqrt_mod
def A116267_gen(): # generator of terms
    for j in count(0):
        b = 10**j
        a = b*10+1
        for k in sorted(sqrt_mod(1,a,all_roots=True)):
            if a*(b+3) <= k**2-1 < a*(a+2):
                yield k-2
A116267_list = list(islice(A116267_gen(),20)) # Chai Wah Wu, Feb 19 2024

Extensions

a(29)-a(32) from Chai Wah Wu, Feb 19 2024