A116136 Numbers k such that k concatenated with k-3 gives the product of two numbers which differ by 4.

9, 99, 183, 328, 528, 715, 999, 6099, 9999, 13224, 40495, 99999, 106755, 453288, 999999, 2066115, 2975208, 9999999, 22145328, 28027683, 99999999, 110213248, 110667555, 147928995, 178838403, 226123528, 275074575, 333052608, 378698224, 445332888, 446245635, 518348515

Offset

1,1

Comments

Also numbers k such that k concatenated with itself gives the product of two numbers which differ by 2.

Links

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

Example

8315420899//8315420896 = 9118892968 * 9118892972, where // denotes concatenation.

Prog

(Python)
from itertools import count, islice
from sympy import sqrt_mod
def A116136_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**2-1)//a
A116136_list = list(islice(A116136_gen(), 40)) # Chai Wah Wu, Feb 19 2024

Crossrefs

Cf. A116129, A115431, A116099, A115426, A116267.

Cf. also A102567, A116154, A116130, A116286.

Sequence in context: A083835 A305670 A045644 * A139280 A292449 A292739

Adjacent sequences: A116133 A116134 A116135 * A116137 A116138 A116139

Keyword

nonn,base

Author

Giovanni Resta, Feb 06 2006

Extensions

Edited by N. J. A. Sloane, Apr 15 2007

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

Status

approved