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A115426
Numbers k such that the concatenation of k with k+2 gives a square.
25
7874, 8119, 69476962, 98010199, 108746354942, 449212110367, 544978035127, 870501316279, 998001001999, 1428394731903223, 1499870932756487, 1806498025502498, 1830668275445687, 1911470478658759, 2255786189655202
OFFSET
1,1
COMMENTS
Numbers k such that k concatenated with k+1 gives the product of two numbers which differ by 2.
Numbers k such that k concatenated with k-2 gives the product of two numbers which differ by 4.
Numbers k such that k concatenated with k-7 gives the product of two numbers which differ by 6.
EXAMPLE
8119//8121 = 9011^2, where // denotes concatenation.
98010199//98010200 = 99000100 * 99000102.
98010199//98010197 = 99000099 * 99000103.
PROG
(Python)
from itertools import count, islice
from sympy import sqrt_mod
def A115426_gen(): # generator of terms
for j in count(0):
b = 10**j
a = b*10+1
for k in sorted(sqrt_mod(2, a, all_roots=True)):
if a*(b-2) <= k**2-2 < a*(a-3):
yield (k**2-2)//a
A115426_list = list(islice(A115426_gen(), 40)) # Chai Wah Wu, Feb 20 2024
KEYWORD
base,nonn
AUTHOR
Giovanni Resta, Jan 24 2006
EXTENSIONS
Edited by N. J. A. Sloane, Apr 13 2007
STATUS
approved