A116339
k times k+6 gives the concatenation of two numbers m and m+7.
Original entry on oeis.org
378, 617, 708, 903, 8761, 45456, 54539, 693063, 8181812, 88235288, 327935224, 330669332, 363636365, 418318517, 428571430, 461538455, 538461540, 571428565, 581681478, 636363630, 669330663, 672064771, 691571588
Offset: 1
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f:= proc(d) local S,x;
S:= map(rhs@op,[msolve((x+3)^2 = 16, 10^d+1)]);
end proc:
g:= proc(n,d) local m; m:= ((n+3)^2-16)/(10^d+1)+7; m >= 10^(d-1) and m < 10^d end proc:
sort([seq](op(select(g,f(i),i)),i=2..13)); # Robert Israel, Jan 27 2024
A116341
k times k+8 gives the concatenation of two numbers m and m+7.
Original entry on oeis.org
82, 314, 679, 756, 952, 965, 3205775326418807415637845823789043451, 3230931606745075612526180113373983267, 3750967203300732832735999247776048870, 6249032796699267167264000752223951123, 6769068393254924387473819886626016726, 6794224673581192584362154176210956542
Offset: 1
965 * 973 = 938//945, where // denotes concatenation, so 965 is a term.
-
from itertools import count, islice
from sympy import sqrt_mod
def A116341_gen(): # generator of terms
for j in count(0):
b = 10**j
a = b*10+1
for k in sorted(sqrt_mod(23,a,all_roots=True)):
if a*(b-7) <= k**2-23 < a*(a-8) and k>4:
yield k-4
A116341_list = list(islice(A116341_gen(),20)) # Chai Wah Wu, Feb 21 2024
A116209
Numbers k such that k concatenated with k+7 gives the product of two numbers which differ by 7.
Original entry on oeis.org
1, 13, 41, 653, 2287, 2723, 5491, 23240971, 26823191, 60249661, 1841968537, 2009317771, 3044234903, 3258336353, 8166731261, 9481619237, 1281071245505271100098621541, 1551605670846640136726379653
Offset: 1
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.
A116346
n times n+7 gives the concatenation of two numbers m and m+8.
Original entry on oeis.org
300, 421, 573, 694, 729, 9856, 36356, 63638, 970299, 4545456, 5454538, 88235296, 351069984, 403018036, 493927127, 506072867, 596981958, 648930010, 736842098, 739839101, 766233768, 769230762, 827751189, 857142859
Offset: 1
Showing 1-5 of 5 results.