A116195
Numbers k such that k concatenated with k+5 gives the product of two numbers which differ by 7.
Original entry on oeis.org
7403, 8885, 12563, 41675, 54239, 2353623, 2650793, 7717533, 527390351115, 567933643889, 627121279653, 671264212463, 1335723019653517755, 2049430589972661489, 2995303155542192885, 4026214090447622723
Offset: 1
7717533//7717538 = 8784946 * 8784953, where // denotes concatenation.
A116319
n times n+7 gives the concatenation of two numbers m and m+4.
Original entry on oeis.org
77, 4328, 5666, 9365, 41505566065992219342, 44035313091289689595, 46429818586950933764, 48959565612248404017, 51040434387751595977, 53570181413049066230, 55964686908710310399, 58494433934007780652
Offset: 1
9365 * 9372 = 8776//8780, where // denotes concatenation.
A116325
n times n+6 gives the concatenation of two numbers m and m+5.
Original entry on oeis.org
2, 3, 29, 66, 739, 893, 755004, 789546, 3643103, 6356892, 9084165, 405460897734702723, 416974886220714237, 583025113779285758, 594539102265297272, 920312382883217575, 931826371369229089
Offset: 1
9084165 * 9084171 = 8252210//8252215, where // denotes
concatenation.
A116327
k times k+8 gives the concatenation of two numbers m and m+5.
Original entry on oeis.org
79, 35475530, 41357883, 58642110, 64524463, 3317813164402425001808, 3762581663871761671881, 4019782237714250566387, 4464550737183587236460, 5535449262816412763533, 5980217762285749433606, 6237418336128238328112
Offset: 1
64524463 * 64524471 = 41634068//41634073, where // denotes concatenation, so 64524463 is a term.
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from itertools import count, islice
from sympy import sqrt_mod
def A116327_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-4
A116327_list = list(islice(A116327_gen(),20)) # Chai Wah Wu, Feb 21 2024
A116332
n times n+7 gives the concatenation of two numbers m and m+6.
Original entry on oeis.org
7041, 487249777146, 512750222848, 684330069117
Offset: 1
7041 * 7048 = 4962//4968, where // denotes concatenation.
Showing 1-5 of 5 results.