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
A116294
Numbers k such that k*(k+1) gives the concatenation of two numbers m and m+1.
Original entry on oeis.org
3, 7, 78, 80919, 91809, 326510, 475025, 524975, 673490, 4323777, 4767132, 5232868, 5676223, 4083911141, 4975000250, 5024999750, 5916088859, 9503960496, 9604950396, 4186904462792, 4313465946775, 5686534053225, 5813095537208, 7504715871407, 7631277355390
Offset: 1
80919 * (80919 + 1) = 6547965480, the concatenation of 65479 and 65479 + 1.
-
Union @@ ((x /. List@ ToRules@ Reduce[x (x+1) == 10^# y +y+1 && x>0 && 10^(#-1) <= y+1 < 10^#, {x,y}, Integers]) & /@ Range[13] /. x->{}) (* Giovanni Resta, Jul 08 2018 *)
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.
A116307
Numbers k such that k*(k+1) gives the concatenation of two numbers m and m+3.
Original entry on oeis.org
83, 77394229, 89158935, 36623663376237623663376337, 37633762366336633762366237, 62366237633663366237633763, 63376336623762376336623663, 86194223018927804587702130
Offset: 1
89158935 * 89158936 = 79493157//79493160, where // denotes concatenation.
Showing 1-4 of 4 results.