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 1-4 of 4 results.

A116153 Numbers k such that k concatenated with k-1 gives the product of two numbers which differ by 9.

Original entry on oeis.org

13, 41, 653, 2287, 2723, 5491, 23240971, 26823191, 60249661, 1841968537, 2009317771, 3044234903, 3258336353, 8166731261, 9481619237, 1281071245505271100098621541, 1551605670846640136726379653
Offset: 1

Views

Author

Giovanni Resta, Feb 06 2006

Keywords

Crossrefs

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

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

A116293 Numbers k such that k * (k+9) is the concatenation of a number m with itself.

Original entry on oeis.org

2, 92, 420, 572, 693, 728, 992, 9855, 9992, 36355, 63637, 99992, 970298, 999992, 4545455, 5454537, 9999992, 88235295, 99999992, 351069983, 403018035, 493927126, 506072866, 596981957, 648930009, 736842097, 739839100, 766233767, 769230761, 827751188, 857142858, 860139852, 879699240, 909090910
Offset: 1

Views

Author

Giovanni Resta, Feb 06 2006

Keywords

Comments

From Robert Israel, Apr 09 2025: (Start)
Numbers k such that k * (k + 9) = (10^d + 1) * m for some d and m where m has d digits.
Contains 10^d-8 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,9)),d=1..10)

Extensions

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

A116278 n times n+9 gives the concatenation of two numbers m and m-2.

Original entry on oeis.org

7040, 487249777145, 512750222847, 684330069116
Offset: 1

Views

Author

Giovanni Resta, Feb 06 2006

Keywords

Examples

			7040 * 7049 = 4962//4960, where // denotes concatenation.
		

Crossrefs

Showing 1-4 of 4 results.