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
A116297
Numbers k such that k*(k+4) gives the concatenation of two numbers m and m+1.
Original entry on oeis.org
2, 5, 43, 54, 38161, 61836, 83616, 346978, 653019, 950049, 8647553, 9534263, 8167822281, 9007920990, 9209900790, 9950000499, 4737445289219, 4990568257185, 5009431742812, 5262554710778, 8373808925583
Offset: 1
A116299
n times n+8 gives the concatenation of two numbers m and m+1.
Original entry on oeis.org
40, 53, 40354307, 59645686, 39704957106129738595969799927610, 44505281604832422780051712184759, 45053875613995255103944518907119, 54946124386004744896055481092874, 55494718395167577219948287815234
Offset: 1
59645686 * 59645694 = 35576083//35576084, 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.
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