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.

A116163 Numbers k such that k concatenated with k+1 gives the product of two numbers which differ by 1.

Original entry on oeis.org

1, 5, 61, 65479, 84289, 106609, 225649, 275599, 453589, 1869505, 2272555, 2738291, 3221951, 1667833021, 2475062749, 2525062249, 3500010739, 9032526511, 9225507211, 1753016898055, 1860598847399, 3233666953849, 3379207972471, 5632076031055, 5823639407489
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 3.

Examples

			1 is a member since 12 = 3*4; also 10 = 2*5.
5 is a member since 56 = 7*8; also 54 = 6*9.

Links

Crossrefs

Cf. A116154, A115426, A116170, A116294.
Cf. A116143, A102567, A116112, A116130, A116280.

Programs

  • Mathematica
    Union @@ ((y /. List@ ToRules@ Reduce[x (x+1) == 10^# y +y+1 && x>0 && 10^(#-1) <= y+1 < 10^#, {x,y}, Integers]) & /@ Range[13] /. y->{}) (* Giovanni Resta, Jul 08 2018 *)

Extensions

Edited by N. J. A. Sloane, Apr 15 2007, Jun 27 2009
More terms from Giovanni Resta, Jul 08 2018

A116287 Numbers k such that k*(k+3) gives the concatenation of a number m with itself.

Original entry on oeis.org

8, 98, 767, 858, 910, 998, 3285, 6713, 9998, 45452, 54546, 99998, 990100, 999998, 8181819, 9999998, 70588233, 99999998, 343130554, 362637363, 363636361, 420053631, 421052632, 497975709, 502024289, 578947366, 579946367, 636363637, 637362635, 656869444, 706766918, 713286714, 714285712, 783689995
Offset: 1

Views

Author

Giovanni Resta, Feb 06 2006

Keywords

Comments

From Robert Israel, Apr 08 2025: (Start)
Numbers k such that k * (k + 3) = (10^d + 1) * m for some d and m where m has d digits.
Contains 10^d-2 for all d >= 1. (End)

Links

Crossrefs

Cf. A116130, A116280, A116286, A116288, A116296.

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,3)),d=1..10); # Robert Israel, Apr 08 2025

Extensions

More terms from Robert Israel, Apr 08 2025

A116274 Numbers k such that k*(k+3) gives the concatenation of two numbers m and m-2.

Original entry on oeis.org

9, 99, 362, 636, 713, 922, 999, 8904, 9999, 81817, 99999, 336632, 663366, 999999, 7272726, 9999999, 76470588, 99999999, 333666332, 405436667, 428571428, 447710184, 454545453, 473684210, 526315788, 545454545, 552289814
Offset: 1

Views

Author

Giovanni Resta, Feb 06 2006

Keywords

Crossrefs

Cf. A116143, A116259, A116273, A116275, A116280.

A116281 Numbers k such that k*(k+5) gives the concatenation of two numbers m and m-1.

Original entry on oeis.org

39, 57, 32262231, 67737765, 79321055, 3341093417798787499092, 3861488851737861033960, 4747922651210186579786, 5252077348789813420210, 6138511148262138966036, 6658906582201212500904, 7232275368591793618230
Offset: 1

Views

Author

Giovanni Resta, Feb 06 2006

Keywords

Examples

			79321055 * 79321060 = 62918301//62918300, where // denotes concatenation.

Crossrefs

Cf. A028557, A116112, A116276, A116280, A116282, A116289.

A116279 Numbers k such that k*(k+2) gives the concatenation of two numbers m and m-1.

Original entry on oeis.org

36363636363, 45454545454, 54545454545, 63636363636, 72727272727, 81818181818, 90909090909, 428571428571428571428, 571428571428571428571, 714285714285714285714, 857142857142857142857
Offset: 1

Views

Author

Giovanni Resta, Feb 06 2006

Keywords

Examples

			36363636363 * 36363636365 = 13223140496//13223140495, where // denotes concatenation.

Crossrefs

Cf. A102567, A116273, A116280, A116286.
Showing 1-5 of 5 results.

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

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