A115428
Numbers k such that the concatenation of k with k+5 gives a square.
Original entry on oeis.org
1, 4, 20, 31, 14564, 38239, 69919, 120395, 426436, 902596, 7478020, 9090220, 6671332084, 8114264059, 8482227259, 9900250996, 2244338786836, 2490577152964, 2509440638591, 2769448208395, 7012067592220
Offset: 1
Cf.
A030465,
A102567,
A115426,
A115437,
A115429,
A115430,
A115431,
A115432,
A115433,
A115434,
A115435,
A115436,
A115439.
A116112
Numbers k such that k concatenated with k-7 gives the product of two numbers which differ by 7.
Original entry on oeis.org
17, 35, 10408517, 45884051, 62918301, 1116290522645838319925, 1491109615209578451401, 2254276950187476704727, 2758431647767103545151, 3768131911733856383477, 4434103687048263321737, 5230580700713956424051
Offset: 1
62918301//62918300 = 79321055 * 79321060, where // denotes concatenation.
62918301//62918304 = 79321056 * 79321059.
62918301//62918306 = 79321057 * 79321058.
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.
A116172
Numbers k such that k concatenated with k+2 gives the product of two numbers which differ by 5.
Original entry on oeis.org
2, 74, 59264, 510782, 906902, 81790664, 92776472, 10876856041862, 11796926254874, 18332259798794, 18388650720624, 32624670587648, 32699883214248, 43103618706398, 44916698243804, 66132258426302
Offset: 1
92776472//92776474 = 96320542 * 96320547, where // denotes concatenation.
92776472//92776480 = 96320544 * 96320545.
92776472//92776478 = 96320543 * 96320546.
A116170
Numbers k such that k concatenated with k+2 gives the product of two numbers which differ by 1.
Original entry on oeis.org
590, 738, 830, 1080, 4508, 20660, 29754, 980300, 6694218, 49826988, 117738578, 131505858, 132231404, 176445054, 177285320, 247979808, 252028388, 335180054, 336337790, 404958680, 406231130, 431477468, 499519478
Offset: 1
-
As:= {}:
for m from 2 to 20 do
acands:= map(t -> rhs(op(t)), [msolve(a*(a+1)=2, 10^m+1)]);
bcands:= map(t -> t*(t+1) mod 10^m, acands);
good:= select(t -> bcands[t]>=10^(m-1), [$1..nops(acands)]);
As:= As union convert(bcands[good], set);
od: map(t -> t-2, sort(convert(As, list))); # Robert Israel, Aug 20 2019
A116302
Numbers k such that k*(k+3) gives the concatenation of two numbers m and m+2.
Original entry on oeis.org
27, 71, 79822844, 69852478553064869297984899963806, 77473062193002372448027740546438, 77747359197583788609974143907618, 84341826458653210947638195982114, 85367942837521291760016984490250
Offset: 1
79822844 * 79822847 = 63716866//63716868, where // denotes concatenation.
A116314
Numbers k such that k*(k+1) gives the concatenation of two numbers m and m+4.
Original entry on oeis.org
28, 72, 79822845, 69852478553064869297984899963807, 77473062193002372448027740546439, 77747359197583788609974143907619, 84341826458653210947638195982115, 85367942837521291760016984490251
Offset: 1
79822845 * 79822846 = 63716866//63716870, where // denotes concatenation.
Showing 1-7 of 7 results.
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