A116202 Numbers k such that k concatenated with k+6 gives the product of two numbers which differ by 8.

7, 54, 234, 267, 894, 58227, 7962242238271227055830015496107, 60153956829051761181170060654114714579377214308482459, 2019668016997743800626449453386765007975459365956534868322001037107, 3031524678136833532602149525055953135725227119574025423809994922862

Offset

1,1

Links

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

Example

58227//58233 = 76303 * 76311, where // denotes concatenation.

Prog

(Python)
from itertools import count, islice
from sympy import sqrt_mod
def A116202_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**2-22)//a
A116202_list = list(islice(A116202_gen(), 7)) # Chai Wah Wu, Feb 21 2024

Crossrefs

Cf. A116196, A116147, A116203, A116210, A116333.

Sequence in context: A372939 A194929 A317689 * A203289 A204258 A081008

Adjacent sequences: A116199 A116200 A116201 * A116203 A116204 A116205

Keyword

nonn,base

Author

Giovanni Resta, Feb 06 2006

Extensions

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

Status

approved