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.
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
A116296
Numbers k such that k*(k+3) gives the concatenation of two numbers m and m+1.
Original entry on oeis.org
82, 77394228, 89158934, 36623663376237623663376336, 37633762366336633762366236, 62366237633663366237633762, 63376336623762376336623662, 86194223018927804587702129
Offset: 1
89158934 * 89158937 = 79493157//79493158, where // denotes concatenation.
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
A116303
n times n+5 gives the concatenation of two numbers m and m+2.
Original entry on oeis.org
3, 84, 76981, 714688, 952312, 90438189, 96320542, 32980078899027, 34346653774236, 42816188292271, 42881990066486, 57118009933510, 57183811707725, 65653346225760, 67019921100969, 81321742742208
Offset: 1
96320542 * 96320547 = 92776472//92776474, where // denotes
concatenation.
Showing 1-5 of 5 results.
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