A116179
Numbers k such that k concatenated with k+3 gives the product of two numbers which differ by 5.
Original entry on oeis.org
1, 3, 81, 1353, 3997, 7723, 23761, 26271, 76771, 1415683, 3890571, 8495497, 1066870443, 1239366513, 4198438981, 4534273891, 6502317141, 6918679731, 2199164200036329043, 2820114781174460091, 5500888421709400741
Offset: 1
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
A116324
Numbers k such that k * (k+5) gives the concatenation of two numbers m and m+5.
Original entry on oeis.org
31, 65, 42754, 57242, 75424, 425073, 574923, 979529, 4301394, 5698602, 7028667, 4925000748, 5074999248, 7748266575, 8511881485, 8814851185, 7059602159673, 7106167933829, 7439286611622, 7485852385778, 46791112884926
Offset: 1
-
f:= proc(d) local S,R,r,s,m,n;
r:= 10^d+1;
S:= map(t -> rhs(op(t)), [msolve(n*(n+5)=5,r)]);
S:= select(proc(s) local t; t:= (s*(s+5)-5)/r; t+5 >= (r-1)/10 and t+5 < r-1 end proc, S);
op(sort(S));
end proc:
map(f, [$1..20]); # Robert Israel, Jun 21 2024
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.
A116311
Numbers k such that k*(k+7) gives the concatenation of two numbers m and m+3.
Original entry on oeis.org
8445, 8810, 69125298546226023971, 69855225553525294044, 74604750601020544519, 75334677608319814592, 92496418993920707746, 93226346001219977819, 97975871048715228294, 98705798056014498367
Offset: 1
8810 * 8817 = 7767//7770, where // denotes concatenation.
Showing 1-5 of 5 results.