A116107
Numbers k such that k concatenated with k-8 gives the product of two numbers which differ by 7.
Original entry on oeis.org
52, 63716866, 48793687600063875363014809897052, 60020753655608135708762056127156, 60446518621981165303188950156776, 71135436903815748345367595855336, 72876856643103028189103298533248
Offset: 1
63716866//63716864 = 79822843 * 79822848, where // denotes concatenation.
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
A116275
Numbers k such that k*(k+4) gives the concatenation of two numbers m and m-2.
Original entry on oeis.org
8872, 9009, 83352840, 99000099, 329767122286, 670232877711, 738226276371, 933006600339, 999000000999, 3779410975143113, 3872816717528065, 4250291784692548, 4278630943941865, 4372036686326817, 4749511753491300, 5250488246508697, 5627963313673180, 5721369056058132
Offset: 1
99000099 * 99000103 = 98010199//98010197, where // denotes concatenation.
-
from itertools import count, islice
from sympy import sqrt_mod
def A116275_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+3) <= k**2-2 < a*(a+2):
yield k-2
A116275_list = list(islice(A116275_gen(),30)) # Chai Wah Wu, Feb 19 2024
A116277
n times n+8 gives the concatenation of two numbers m and m-2.
Original entry on oeis.org
65, 738, 892, 755003, 789545, 3643102, 6356891, 9084164, 405460897734702722, 416974886220714236, 583025113779285757, 594539102265297271, 920312382883217574, 931826371369229088, 4330823773309769374
Offset: 1
9084164 * 9084172 = 8252210//8252208, where // denotes
concatenation.
A116281
Numbers k such that k*(k+5) gives the concatenation of two numbers m and m-1.
Original entry on oeis.org
39, 57, 32262231, 67737765, 79321055, 3341093417798787499092, 3861488851737861033960, 4747922651210186579786, 5252077348789813420210, 6138511148262138966036, 6658906582201212500904, 7232275368591793618230
Offset: 1
79321055 * 79321060 = 62918301//62918300, where // denotes concatenation.
Showing 1-5 of 5 results.
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