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.

A116290 Numbers k such that k * (k+6) is the concatenation of a number m with itself.

Original entry on oeis.org

5, 95, 462, 533, 715, 819, 995, 3425, 6570, 9995, 90904, 99995, 980199, 999995, 3636358, 6363637, 9999995, 41176465, 58823530, 99999995, 413533835, 426573427, 428571423, 432620006, 567379989, 571428572, 573426568, 586466160, 686261108, 725274726, 727272722
Offset: 1

Views

Author

Giovanni Resta, Feb 06 2006

Keywords

Comments

From Robert Israel, Apr 08 2025: (Start)
Numbers k such that k * (k + 6) = (10^d + 1) * m for some d and m where m has d digits.
Contains 10^d-5 for all d >= 1. (End)

Links

Crossrefs

Cf. A116159, A116282, A116289, A116291, A116304.

Programs

  • Maple
    f:= proc(d) 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,-6],[a,b]) by t do
       q:= x*(x+6)/t;
       if q >= 10^d then break fi;
       if q >= 10^(d-1) then R:= R, x fi;
   od od;
   sort([R]);
end proc:
seq(op(f(d)),d=1..10); # Robert Israel, Apr 08 2025

Extensions

Name edited by Robert Israel, Apr 08 2025

A116292 Numbers k such that k * (k + 8) is the concatenation of a number m with itself.

Original entry on oeis.org

3, 93, 377, 616, 707, 902, 993, 8760, 9993, 45455, 54538, 99993, 693062, 999993, 8181811, 9999993, 88235287, 99999993, 327935223, 330669331, 363636364, 418318516, 428571429, 461538454, 538461539, 571428564, 581681477, 636363629, 669330662, 672064770, 691571587, 756506652, 781954880, 789473685
Offset: 1

Views

Author

Giovanni Resta, Feb 06 2006

Keywords

Comments

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

Links

Crossrefs

Cf. A116161, A116277, A116291, A116293, A116299.

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,8)),d=1..10); # Robert Israel, Apr 09 2025
  • Mathematica
    ccnQ[n_]:=With[{ccc=With[{c=n(n+8)},TakeDrop[IntegerDigits[c],IntegerLength[c]/2]]},ccc[[1]]==ccc[[2]]];  Select[Range[10^6],ccnQ]//Quiet (* The program generates the first 14 terms of the sequence. *) (* Harvey P. Dale, Jul 05 2025 *)

Extensions

Name edited and more terms from Robert Israel, Apr 09 2025

A116160 Numbers k such that k concatenated with itself gives the product of two numbers which differ by 7.

Original entry on oeis.org

4, 94, 210, 294, 994, 5880, 9994, 52888, 99994, 127044, 414180, 999994, 8264470, 9999994, 12456750, 41868508, 99999994, 112670544, 441341880, 468144040, 669421494, 702338994, 715976338, 750005718, 960645294, 999999994
Offset: 1

Views

Author

Giovanni Resta, Feb 06 2006

Keywords

Crossrefs

Cf. A020338, A116152, A116159, A116161, A116167, A116291.

A116283 k times k+7 gives the concatenation of two numbers m and m-1.

Original entry on oeis.org

7, 30, 64, 42753, 57241, 75423, 425072, 574922, 979528, 4301393, 5698601, 7028666, 4925000747, 5074999247, 7748266574, 8511881484, 8814851184, 7059602159672, 7106167933828, 7439286611621, 7485852385777
Offset: 1

Views

Author

Giovanni Resta, Feb 06 2006

Keywords

Crossrefs

Cf. A001704, A028563.
Cf. A116152, A116269, A116282, A116284, A116291.

Programs

  • Python
    def ok(n):
    s = str(n*(n+7)); h = (len(s)+1)//2; return int(s[:h])-1 == int(s[h:])
print(list(filter(ok, range(2, 10**6)))) # Michael S. Branicky, Jul 30 2021

A116298 n times n+7 gives the concatenation of two numbers m and m+1.

Original entry on oeis.org

6, 699, 776, 790, 867, 42337, 57657, 96883, 44121666, 55878328, 85298137, 36680703009575609347721358493, 63319296990424390652278641501, 69346342454876071597336150481, 81501115172242572470460459683
Offset: 1

Views

Author

Giovanni Resta, Feb 06 2006

Keywords

Examples

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

Crossrefs

Cf. A116167, A116291, A116297, A116299, A116311.
Showing 1-5 of 5 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.