cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-5 of 5 results.

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

Views

Author

Giovanni Resta, Feb 06 2006

Keywords

Examples

			72757727//72757728 = 85298137 * 85298144, where // denotes concatenation.
		

Crossrefs

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

Views

Author

Giovanni Resta, Feb 06 2006

Keywords

Comments

From Robert Israel, Apr 09 2025: (Start)
Numbers k such that k * (k + 7) = (10^d + 1) * m for some d and m where m has d digits.
Contains 10^d - 6 for all d >= 1. (End)

Crossrefs

Programs

  • Maple
    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

Views

Author

Giovanni Resta, Feb 06 2006

Keywords

Crossrefs

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

Views

Author

Giovanni Resta, Feb 06 2006

Keywords

Crossrefs

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

Views

Author

Giovanni Resta, Feb 06 2006

Keywords

Crossrefs

Showing 1-5 of 5 results.