A116167
Numbers k such that k concatenated with k+1 gives the product of two numbers which differ by 7.
Original entry on oeis.org
7, 493, 607, 629, 757, 17927, 33247, 93869, 19467217, 31223879, 72757727, 13454739732766891651472740499, 40093333713615672956030023507, 48089152118689474641229584727, 66424317743191484432891678269
Offset: 1
72757727//72757728 = 85298137 * 85298144, where // denotes concatenation.
A116291
Numbers k such that k * (k + 7) is the concatenation of a number m with itself.
Original entry on oeis.org
4, 94, 455, 539, 994, 7665, 9994, 72721, 99994, 356429, 643565, 999994, 9090910, 9999994, 35294118, 64705876, 99999994, 335664329, 664335665, 684210520, 818181819, 838056674, 846153847, 866028702, 980125139, 999999994
Offset: 1
-
q:= proc(d,m) local R,t,a,b,x,q;
t:= 10^d+1;
R:= NULL;
for a in numtheory:-divisors(t) do
b:= t/a;
if igcd(a,b) > 1 then next fi;
for x from chrem([0,-m],[a,b]) by t do
q:= x*(x+m)/t;
if q >= 10^d then break fi;
if q >= 10^(d-1) then R:= R, x fi;
od od;
sort(convert({R},list));
end proc:
[seq(op(q(d,7)),d=1..10)]; # Robert Israel, Apr 09 2025
A116152
Numbers k such that k concatenated with k-1 gives the product of two numbers which differ by 7.
Original entry on oeis.org
9, 11, 45, 18281, 32769, 56891, 180689, 330539, 959481, 1850201, 3247409, 4940219, 2425563239, 2575561739, 6003563495, 7245212645, 7770160145, 4983798265289, 5049762270381, 5534298528989, 5603798594169
Offset: 1
A116159
Numbers k such that k concatenated with itself gives the product of two numbers which differ by 6.
Original entry on oeis.org
5, 95, 216, 287, 515, 675, 995, 1175, 4320, 9995, 82640, 99995, 960795, 999995, 1322312, 4049591, 9999995, 16955015, 34602080, 99999995, 171010235, 181964891, 183673467, 187160072, 321920055, 326530616, 328818032
Offset: 1
A116161
Numbers k such that k concatenated with itself gives the product of two numbers which differ by 8.
Original entry on oeis.org
3, 93, 145, 384, 505, 820, 993, 7680, 9993, 20665, 29748, 99993, 480340, 999993, 6694209, 9999993, 77854665, 99999993, 107541513, 109342209, 132231408, 174990384, 183673473, 213017748, 289940833, 326530608, 338353345
Offset: 1
Showing 1-5 of 5 results.
Comments