A116205
Numbers k such that k concatenated with k+7 gives the product of two numbers which differ by 3.
Original entry on oeis.org
1, 81, 1353, 3997, 7723, 23761, 26271, 76771, 1415683, 3890571, 8495497, 1066870443, 1239366513, 4198438981, 4534273891, 6502317141, 6918679731, 2199164200036329043, 2820114781174460091, 5500888421709400741
Offset: 1
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
A116263
n times n+7 gives the concatenation of two numbers m and m-4.
Original entry on oeis.org
83, 76980, 714687, 952311, 90438188, 96320541, 32980078899026, 34346653774235, 42816188292270, 42881990066485, 57118009933509, 57183811707724, 65653346225759, 67019921100968, 81321742742207
Offset: 1
96320541 * 96320548 = 92776472//92776468, where // denotes
concatenation.
A116270
n times n+8 gives the concatenation of two numbers m and m-3.
Original entry on oeis.org
62, 45211539, 54788454, 78317866, 72388446037855609175404256, 73247326752475247326752671, 75267524732673267524732471, 76126405447292905676080886, 42053270820132695893502981749302
Offset: 1
78317866 * 78317874 = 61336887//61336884, where // denotes
concatenation.
A116283
k times k+7 gives the concatenation of two numbers m and m-1.
Original entry on oeis.org
7, 30, 64, 42753, 57241, 75423, 425072, 574922, 979528, 4301393, 5698601, 7028666, 4925000747, 5074999247, 7748266574, 8511881484, 8814851184, 7059602159672, 7106167933828, 7439286611621, 7485852385777
Offset: 1
-
def ok(n):
s = str(n*(n+7)); h = (len(s)+1)//2; return int(s[:h])-1 == int(s[h:])
print(list(filter(ok, range(2, 10**6)))) # Michael S. Branicky, Jul 30 2021
Showing 1-5 of 5 results.
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