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.
A116163
Numbers k such that k concatenated with k+1 gives the product of two numbers which differ by 1.
Original entry on oeis.org
1, 5, 61, 65479, 84289, 106609, 225649, 275599, 453589, 1869505, 2272555, 2738291, 3221951, 1667833021, 2475062749, 2525062249, 3500010739, 9032526511, 9225507211, 1753016898055, 1860598847399, 3233666953849, 3379207972471, 5632076031055, 5823639407489
Offset: 1
1 is a member since 12 = 3*4; also 10 = 2*5.
5 is a member since 56 = 7*8; also 54 = 6*9.
-
Union @@ ((y /. List@ ToRules@ Reduce[x (x+1) == 10^# y +y+1 && x>0 && 10^(#-1) <= y+1 < 10^#, {x,y}, Integers]) & /@ Range[13] /. y->{}) (* Giovanni Resta, Jul 08 2018 *)
A116171
Numbers k such that k concatenated with k+2 gives the product of two numbers which differ by 3.
Original entry on oeis.org
8, 52, 63716866, 48793687600063875363014809897052, 60020753655608135708762056127156, 60446518621981165303188950156776, 71135436903815748345367595855336, 72876856643103028189103298533248
Offset: 1
63716866//63716868 = 79822844 * 79822847, where // denotes concatenation.
63716866//63716870 = 79822845 * 79822846.
A116301
n times n+1 gives the concatenation of two numbers m and m+2.
Original entry on oeis.org
768, 859, 911, 3286, 6714, 45453, 54547, 990101, 8181820, 70588234, 343130555, 362637364, 363636362, 420053632, 421052633, 497975710, 502024290, 578947367, 579946368, 636363638, 637362636, 656869445, 706766919
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(acands[good],set);
od:
sort(convert(As,list)); # Robert Israel, Aug 20 2019
Showing 1-4 of 4 results.
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