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.

A116112 Numbers k such that k concatenated with k-7 gives the product of two numbers which differ by 7.

Original entry on oeis.org

17, 35, 10408517, 45884051, 62918301, 1116290522645838319925, 1491109615209578451401, 2254276950187476704727, 2758431647767103545151, 3768131911733856383477, 4434103687048263321737, 5230580700713956424051
Offset: 1

Views

Author

Giovanni Resta, Feb 06 2006

Keywords

Comments

Also numbers k such that k concatenated with k-1 gives the product of two numbers which differ by 5.
Also numbers k such that k concatenated with k+3 gives the product of two numbers which differ by 3.
Also numbers k such that k concatenated with k+5 gives the product of two numbers which differ by 1.

Examples

			62918301//62918300 = 79321055 * 79321060, where // denotes concatenation.
62918301//62918304 = 79321056 * 79321059.
62918301//62918306 = 79321057 * 79321058.

Crossrefs

Cf. A116107, A115426, A116113, A116119, A116243.
Cf. A116163, A115429, A116158, A116281.
Cf. A116171, A116177, A116179, A116185, A116309, A115430, A116322.

Extensions

Edited by N. J. A. Sloane, Apr 15 2007

A116172 Numbers k such that k concatenated with k+2 gives the product of two numbers which differ by 5.

Original entry on oeis.org

2, 74, 59264, 510782, 906902, 81790664, 92776472, 10876856041862, 11796926254874, 18332259798794, 18388650720624, 32624670587648, 32699883214248, 43103618706398, 44916698243804, 66132258426302
Offset: 1

Views

Author

Giovanni Resta, Feb 06 2006

Keywords

Comments

Also numbers k such that k concatenated with k+6 gives the product of two numbers which differ by 3.
Also numbers k such that k concatenated with k+8 gives the product of two numbers which differ by 1.
If k+2 and k-4 have the same number of digits, then k is also in A116132 because k//k+2 = 10^d*k + k + 2 = m*(m+5) then implies k//k-4 = 10^d*k + k - 4 = m*(m+5) - 6 = (m-1)*(m+6). - R. J. Mathar, Aug 10 2008

Examples

			92776472//92776474 = 96320542 * 96320547, where // denotes concatenation.
92776472//92776480 = 96320544 * 96320545.
92776472//92776478 = 96320543 * 96320546.

Crossrefs

Cf. A116158, A116171, A116173, A116179, A116303.
Cf. A116185, A115430, A116205, A116343, A116200, A116330.

Extensions

Edited by N. J. A. Sloane, Apr 15 2007

A116125 Numbers k such that k concatenated with k-5 gives the product of two numbers which differ by 6.

Original entry on oeis.org

7, 97, 205, 300, 477, 732, 997, 1920, 3157, 9997, 52896, 99997, 120085, 427020, 999997, 8264460, 9999997, 88581312, 99999997, 112000885, 112917765, 143075580, 152863360, 193537077, 233788192, 266755221, 313680096
Offset: 1

Views

Author

Giovanni Resta, Feb 06 2006

Keywords

Comments

Also numbers k such that k concatenated with itself gives the product of two numbers which differ by 4.

Examples

			6786111717//6786111712 = 8237785936 * 8237785942, where // denotes concatenation.

Crossrefs

Cf. A115426, A116124, A116126, A116131, A116256.
Cf. A116130, A116158, A115428, A116288.

Extensions

Edited by N. J. A. Sloane, Apr 15 2007

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

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.
Showing 1-5 of 5 results.

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

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