A116147
Numbers k such that k concatenated with k-2 gives the product of two numbers which differ by 9.
Original entry on oeis.org
4962, 237412345332, 262912791034, 468307643502
Offset: 1
4962//4960 = 7040 * 7049, where // denotes concatenation.
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.
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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
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.
A116331
n times n+5 gives the concatenation of two numbers m and m+6.
Original entry on oeis.org
456, 540, 7666, 72722, 356430, 643566, 9090911, 35294119, 64705877, 335664330, 664335666, 684210521, 818181820, 838056675, 846153848, 866028703, 980125140, 3861386140, 6138613856, 6916125390, 9222488468, 41358246491
Offset: 1
A116340
n times n+7 gives the concatenation of two numbers m and m+7.
Original entry on oeis.org
2, 33, 61, 805, 4779, 5215, 7407, 48208887, 51791107, 77620652, 4291816089, 4482541431, 5517458563, 5708183905, 9036996877, 9737360644, 3579205562000136225339579332, 3939042613182345526485238180
Offset: 1
Showing 1-5 of 5 results.
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