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

Author

Giovanni Resta, Feb 06 2006

Keywords

• nonn
• base

Comments

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

Examples

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

Links

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

Crossrefs

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

Cf. also A102567, A116154, A116130, A116286.

Programs

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

Extensions

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

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