A116295
Numbers k such that k*(k+2) gives the concatenation of two numbers m and m+1.
Original entry on oeis.org
8873, 9010, 83352841, 99000100, 329767122287, 670232877712, 738226276372, 933006600340, 999000001000, 3779410975143114, 3872816717528066, 4250291784692549, 4278630943941866, 4372036686326818, 4749511753491301
Offset: 1
99000100 * 99000102 = 98010199//98010200, where // denotes concatenation.
-
Res:= NULL:
for d from 1 to 40 do
Res:= Res, op(sort(select(t -> t^2 >= 10^(2*d-1),map(t -> rhs(op(t))-1,[msolve(x^2=2, 10^d+1)]))))
od:
Res; # Robert Israel, Jun 06 2018
A116309
Numbers k such that k*(k+3) gives the concatenation of two numbers m and m+3.
Original entry on oeis.org
40, 58, 32262232, 67737766, 79321056, 3341093417798787499093, 3861488851737861033961, 4747922651210186579787, 5252077348789813420211, 6138511148262138966037, 6658906582201212500905, 7232275368591793618231
Offset: 1
79321056 * 79321059 = 62918301//62918304, where // denotes concatenation.
-
As:= {}:
for m from 2 to 62 do
acands:= map(t -> rhs(op(t)), [msolve(a*(a+3)=3, 10^m+1)]);
bcands:= map(t -> t*(t+3) 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
A116315
Numbers k such that k*(k+2) gives the concatenation of two numbers m and m+4.
Original entry on oeis.org
3, 6, 44, 55, 38162, 61837, 83617, 346979, 653020, 950050, 8647554, 9534264, 8167822282, 9007920991, 9209900791, 9950000500, 4737445289220, 4990568257186, 5009431742813, 5262554710779, 8373808925584
Offset: 1
A116177
Numbers k such that k concatenated with k+3 gives the product of two numbers which differ by 2.
Original entry on oeis.org
205, 300, 477, 732, 1920, 3157, 52896, 120085, 427020, 8264460, 88581312, 112000885, 112917765, 143075580, 152863360, 193537077, 233788192, 266755221, 313680096, 370908477, 386568925, 440852992, 442670220
Offset: 1
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 1-5 of 5 results.
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