A115430
Numbers k such that the concatenation of k with k+9 gives a square.
Original entry on oeis.org
216, 287, 515, 675, 1175, 4320, 82640, 960795, 1322312, 4049591, 16955015, 34602080, 171010235, 181964891, 183673467, 187160072, 321920055, 326530616, 328818032, 343942560, 470954312, 526023432, 528925616, 534830855
Offset: 1
Cf.
A030465,
A102567,
A115426,
A115437,
A115428,
A115429,
A115431,
A115432,
A115433,
A115434,
A115435,
A115436,
A115441.
A116099
Numbers k such that k concatenated with k-9 gives the product of two numbers which differ by 7.
Original entry on oeis.org
69, 59898667, 79493157, 13412927190959690154913903, 14163000698458955079906403, 38895475965785687555173929, 40165600438484442828161229, 74294440818366638194239027
Offset: 1
79493157//79493154 = 89158933 * 89158938, where // denotes concatenation.
79493157//79493158 = 89158934 * 89158937.
79493157//79493160 = 89158935 * 89158936.
79493157//79493148 = 89158932 * 89158939.
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
A116187
Numbers k such that k concatenated with k+4 gives the product of two numbers which differ by 6.
Original entry on oeis.org
12, 43, 20440836, 30017751, 61336887, 52400871197755334426147587, 53651708763838760619655612, 56652002793835820319625612, 57952296063256269823192087, 17684775866714240650923831481623
Offset: 1
61336887//61336891 = 78317867 * 78317873, where // denotes concatenation. 61336887//61336896 = 78317868 * 78317872.
A116179
Numbers k such that k concatenated with k+3 gives the product of two numbers which differ by 5.
Original entry on oeis.org
1, 3, 81, 1353, 3997, 7723, 23761, 26271, 76771, 1415683, 3890571, 8495497, 1066870443, 1239366513, 4198438981, 4534273891, 6502317141, 6918679731, 2199164200036329043, 2820114781174460091, 5500888421709400741
Offset: 1
A116324
Numbers k such that k * (k+5) gives the concatenation of two numbers m and m+5.
Original entry on oeis.org
31, 65, 42754, 57242, 75424, 425073, 574923, 979529, 4301394, 5698602, 7028667, 4925000748, 5074999248, 7748266575, 8511881485, 8814851185, 7059602159673, 7106167933829, 7439286611622, 7485852385778, 46791112884926
Offset: 1
-
f:= proc(d) local S,R,r,s,m,n;
r:= 10^d+1;
S:= map(t -> rhs(op(t)), [msolve(n*(n+5)=5,r)]);
S:= select(proc(s) local t; t:= (s*(s+5)-5)/r; t+5 >= (r-1)/10 and t+5 < r-1 end proc, S);
op(sort(S));
end proc:
map(f, [$1..20]); # Robert Israel, Jun 21 2024
A116194
Numbers k such that k concatenated with k+5 gives the product of two numbers which differ by 6.
Original entry on oeis.org
1, 2, 10, 47, 550, 802, 570035, 623387, 1327222, 4041011, 8252210, 164398539591831062, 173868055738777586, 339918283297349107, 353476744122425611, 846974882088186070, 868300386379144450
Offset: 1
8252210//8252215 = 9084165 * 9084171, where // denotes
concatenation.
A116200
Numbers k such that k concatenated with k+6 gives the product of two numbers which differ by 5.
Original entry on oeis.org
210, 294, 5880, 52888, 127044, 414180, 8264470, 12456750, 41868508, 112670544, 441341880, 468144040, 669421494, 702338994, 715976338, 750005718, 960645294, 1491030294, 3768258010, 4783279044, 8505429358, 17105045530
Offset: 1
A116109
Numbers k such that k concatenated with k-8 gives the product of two numbers which differ by 9.
Original entry on oeis.org
94, 210, 294, 994, 5880, 9994, 52888, 99994, 127044, 414180, 999994, 8264470, 9999994, 12456750, 41868508, 99999994, 112670544, 441341880, 468144040, 669421494, 702338994, 715976338, 750005718, 960645294, 999999994
Offset: 1
8505429358//8505429350 = 9222488466 * 9222488475, where // denotes concatenation.
A116349
Numbers k such that k*(k+3) gives the concatenation of two numbers m and m+9.
Original entry on oeis.org
32, 66, 42755, 57243, 75425, 425074, 574924, 979530, 4301395, 5698603, 7028668, 4925000749, 5074999249, 7748266576, 8511881486, 8814851186, 7059602159674, 7106167933830, 7439286611623, 7485852385779, 46791112884927
Offset: 1
Showing 1-10 of 11 results.
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