A115426
Numbers k such that the concatenation of k with k+2 gives a square.
Original entry on oeis.org
7874, 8119, 69476962, 98010199, 108746354942, 449212110367, 544978035127, 870501316279, 998001001999, 1428394731903223, 1499870932756487, 1806498025502498, 1830668275445687, 1911470478658759, 2255786189655202
Offset: 1
8119//8121 = 9011^2, where // denotes concatenation.
98010199//98010200 = 99000100 * 99000102.
98010199//98010197 = 99000099 * 99000103.
Cf.
A030465,
A102567,
A115427,
A115428,
A115429,
A115430,
A115431,
A115432,
A115433,
A115434,
A115435,
A115436,
A115437.
-
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
A116103
Numbers k such that k concatenated with k-8 gives the product of two numbers which differ by 3.
Original entry on oeis.org
58, 1552909498221642960203840517299022287877411846, 1723404686015903064905313664707396376746205762, 2153694542826970975147295558223788704098018912
Offset: 1
58//50 = 75 * 78, where // denotes concatenation.
A116122
Numbers k such that k concatenated with k-5 gives the product of two numbers which differ by 3.
Original entry on oeis.org
92185, 1453156572932210152879253333913, 3829098407015032018435618903285, 1017438814759112270449904796121753809
Offset: 1
92185//92180 = 96012 * 96015, where // denotes concatenation.
A116241
n times n+3 gives the concatenation of two numbers m and m-7.
Original entry on oeis.org
73, 7248, 7933, 86896, 95987, 7450774, 8912861, 3546363535354546353, 4635454646463635463, 5364545353536364535, 6453636464645453645, 31993591495513432827263, 39229430087220380122375
Offset: 1
8912861 * 8912864 = 7943911//7943904, where // denotes
concatenation.
Showing 1-4 of 4 results.
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