A116130
Numbers k such that k concatenated with k-4 gives the product of two numbers which differ by 5.
Original entry on oeis.org
8, 98, 590, 738, 830, 998, 1080, 4508, 9998, 20660, 29754, 99998, 980300, 999998, 6694218, 9999998, 49826988, 99999998, 117738578, 131505858, 132231404, 176445054, 177285320, 247979808, 252028388, 335180054, 336337790
Offset: 1
7531357568//7531357564 = 8678339452 * 8678339457, where // denotes concatenation.
A116260
n times n+4 gives the concatenation of two numbers m and m-4.
Original entry on oeis.org
9, 99, 999, 9999, 99999, 999999, 9999999, 99999999, 999999999, 9999999999, 36363636362, 45454545453, 54545454544, 63636363635, 72727272726, 81818181817, 90909090908, 99999999999, 999999999999, 9999999999999
Offset: 1
99999999 * 100000003 = 100000001//99999997, where // denotes concatenation.
-
from itertools import count, islice
from sympy import sqrt_mod
def A116260_gen(): # generator of terms
for j in count(0):
b = 10**j
a = b*10+1
for k in sorted(sqrt_mod(0,a,all_roots=True))+[a]:
if a*(b+4) <= k**2 < a*(a+3):
yield k-2
A116260_list = list(islice(A116260_gen(),20)) # Chai Wah Wu, Feb 19 2024
A116268
Numbers k such that k*(k+5) gives the concatenation of two numbers m and m-3.
Original entry on oeis.org
81, 77394227, 89158933, 36623663376237623663376335, 37633762366336633762366235, 62366237633663366237633761, 63376336623762376336623661, 86194223018927804587702128, 88063202723646452838040443, 35574229497606875609044578088011, 35693849662968953146129859753682, 42317841210726174031503123524229
Offset: 1
89158933 * 89158938 = 79493157//79493154, where // denotes concatenation.
-
f:= proc(d) local k, K;
K:= map(t -> rhs(op(t)), [msolve(k^2+5*k+3=0,10^d+1)]);
op(sort(select(k -> k^2 + 5*k + 3 >= (10^d+1)*10^(d-1), K)));
end proc:
map(f, [$1..62]); # Robert Israel, Jul 10 2025
A116255
n times n+5 gives the concatenation of two numbers m and m-5.
Original entry on oeis.org
76, 80917, 91807, 326508, 475023, 524973, 673488, 4323775, 4767130, 5232866, 5676221, 4083911139, 4975000248, 5024999748, 5916088857, 9503960494, 9604950394, 4186904462790, 4313465946773, 5686534053223, 5813095537206
Offset: 1
A116262
n times n+6 gives the concatenation of two numbers m and m-4.
Original entry on oeis.org
42, 53, 38160, 61835, 83615, 346977, 653018, 950048, 8647552, 9534262, 8167822280, 9007920989, 9209900789, 9950000498, 4737445289218, 4990568257184, 5009431742811, 5262554710777, 8373808925582
Offset: 1
Showing 1-5 of 5 results.
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