A116320
n times n+8 gives the concatenation of two numbers m and m+4.
Original entry on oeis.org
4, 86, 32762, 67231, 76322, 693956, 900097, 7295105, 9068525, 3664355432, 6335644561, 8015841979, 8419801579, 9900000997, 3252382148828, 6747617851165, 7253863787097, 9474890578438, 9981136514370
Offset: 1
-
Res:= NULL: count:= 0:
for d from 1 while count < 100 do
R:= sort(select(t -> t^2 + 8*t - 4 > 10^(2*d-1) and t^2+8*t-4 < 10^(2*d), map(t -> rhs(op(t)), [msolve(n^2+8*n-4, 10^d+1)])));
count := count+nops(R);
Res:= Res, op(R);
od:
Res; # Robert Israel, Jun 20 2018
A116333
k times k+8 gives the concatenation of two numbers m and m+6.
Original entry on oeis.org
23, 70, 480, 513, 942, 76303, 8923139715521228493004072379869, 77558981961505761619171327422086381910161500424346805, 4494071669430455134012149964165405936125116123191254722256003057119, 5505928330569544865987850035834594063874883876808745277743996942874
Offset: 1
76303 * 76311 = 58227//58233, where // denotes concatenation, so 76303 is a term.
-
from itertools import count, islice
from sympy import sqrt_mod
def A116333_gen(): # generator of terms
for j in count(0):
b = 10**j
a = b*10+1
for k in sorted(sqrt_mod(22,a,all_roots=True)):
if a*(b-6) <= k**2-22 < a*(a-7) and k>4:
yield k-4
A116333_list = list(islice(A116333_gen(),10)) # Chai Wah Wu, Feb 21 2024
A116196
Numbers k such that k concatenated with k+5 gives the product of two numbers which differ by 8.
Original entry on oeis.org
68, 12585135, 17104748, 34388975, 41634068, 1100788419388203283323, 1415702077730399453204, 1615864923864298764860, 1993221328488651223275, 3064119854121476750348, 3576300448435797632079, 3890538749986876109435
Offset: 1
41634068//41634073 = 64524463 * 64524471, where // denotes concatenation.
-
from itertools import count, islice
from sympy import sqrt_mod
def A116196_gen(): # generator of terms
for j in count(0):
b = 10**j
a = b*10+1
for k in sorted(sqrt_mod(21,a,all_roots=True)):
if a*(b-5) <= k**2-21 < a*(a-6) and k>4:
yield (k**2-21)//a
A116196_list = list(islice(A116196_gen(),10)) # Chai Wah Wu, Feb 21 2024
A116326
Numbers k such that k*(k+7) gives the concatenation of two numbers m and m+5.
Original entry on oeis.org
8601, 9423, 35441, 64553, 73644, 4851412, 5148582, 8784946, 726216462985, 753613723259, 791909893642, 819307153916, 3654754464602947513, 4527063717215234299, 5472936282784765695, 6345245535397052481
Offset: 1
8784946 * 8784953 = 7717533//7717538, where // denotes concatenation.
A116328
n times n+9 gives the concatenation of two numbers m and m+5.
Original entry on oeis.org
46, 4947936213, 5052063779, 9742829100, 32730757363062987012674789, 67269242636937012987325203, 99706862598549297056423092, 3163201195414530993427385140698350
Offset: 1
Showing 1-5 of 5 results.
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