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.

A116289 Numbers k such that k*(k+5) gives the concatenation of a number m with itself.

Original entry on oeis.org

6, 96, 385, 429, 567, 611, 814, 996, 4521, 5475, 9996, 90910, 99996, 316832, 683164, 999996, 3636364, 6363632, 9999996, 82352942, 99999996, 331668332, 368421053, 395604391, 442767754, 461538462, 488721800, 511278196, 538461534, 557232242, 604395605, 631578943, 668331664, 700089385, 727272728
Offset: 1

Views

Author

Giovanni Resta, Feb 06 2006

Keywords

Comments

From Robert Israel, Apr 09 2025: (Start)
Numbers k such that k * (k + 5) = (10^d + 1) * m for some d and m where m has d digits.
Contains 10^d-4 for all d >= 1. (End)

Links

Crossrefs

Cf. A028557, A020338.
Cf. A116158, A116281, A116288, A116290, A116303.

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,5)),d=1..10); # Robert Israel, Apr 09 2025

Extensions

More terms from Robert Israel, Apr 09 2025

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)

Links

Crossrefs

Cf. A116160, A116283, A116290, A116292, A116298.

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

A116304 Numbers k such that k*(k+6) gives the concatenation of two numbers m and m+2.

Original entry on oeis.org

8217107, 8030443878983905981, 43467818511541680701794365325328847002051, 56532181488458319298205634674671152997944
Offset: 1

Views

Author

Giovanni Resta, Feb 06 2006

Keywords

Examples

			8217107 * 8217113 = 6752089//6752091, where // denotes concatenation.

Crossrefs

Cf. A116173, A116290, A116303, A116305, A116318.

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

Cf. A115429, A116158, A116160, A116173, A116290.

A116282 Numbers k such that k*(k+6) gives the concatenation of two numbers m and m-1.

Original entry on oeis.org

7744, 8018, 33294315, 66705680, 98000198, 340465755422, 476452552742, 523547447253, 659534244573, 866013200678, 998000001998, 3695104677080131, 3755782995538765, 4198081170077528, 4803478892324963, 5196521107675032
Offset: 1

Views

Author

Giovanni Resta, Feb 06 2006

Keywords

Examples

			98000198 * 98000204 = 96040393//96040392, where // denotes concatenation.

Crossrefs

Cf. A115429, A116262, A116281, A116283, A116290.
Showing 1-5 of 5 results.

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