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
A116339
k times k+6 gives the concatenation of two numbers m and m+7.
Original entry on oeis.org
378, 617, 708, 903, 8761, 45456, 54539, 693063, 8181812, 88235288, 327935224, 330669332, 363636365, 418318517, 428571430, 461538455, 538461540, 571428565, 581681478, 636363630, 669330663, 672064771, 691571588
Offset: 1
-
f:= proc(d) local S,x;
S:= map(rhs@op,[msolve((x+3)^2 = 16, 10^d+1)]);
end proc:
g:= proc(n,d) local m; m:= ((n+3)^2-16)/(10^d+1)+7; m >= 10^(d-1) and m < 10^d end proc:
sort([seq](op(select(g,f(i),i)),i=2..13)); # Robert Israel, Jan 27 2024
A116194
Numbers k such that k concatenated with k+5 gives the product of two numbers which differ by 6.
Original entry on oeis.org
1, 2, 10, 47, 550, 802, 570035, 623387, 1327222, 4041011, 8252210, 164398539591831062, 173868055738777586, 339918283297349107, 353476744122425611, 846974882088186070, 868300386379144450
Offset: 1
8252210//8252215 = 9084165 * 9084171, where // denotes
concatenation.
A116318
n times n+6 gives the concatenation of two numbers m and m+4.
Original entry on oeis.org
32, 63, 45211540, 54788455, 78317867, 72388446037855609175404257, 73247326752475247326752672, 75267524732673267524732472, 76126405447292905676080887, 42053270820132695893502981749303
Offset: 1
78317867 * 78317873 = 61336887//61336891, where // denotes
concatenation.
A116326
Numbers k such that k*(k+7) gives the concatenation of two numbers m and m+5.
Original entry on oeis.org
8601, 9423, 35441, 64553, 73644, 4851412, 5148582, 8784946, 726216462985, 753613723259, 791909893642, 819307153916, 3654754464602947513, 4527063717215234299, 5472936282784765695, 6345245535397052481
Offset: 1
8784946 * 8784953 = 7717533//7717538, where // denotes concatenation.
Showing 1-5 of 5 results.