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.

A115429 Numbers k such that the concatenation of k with k+8 gives a square.

Original entry on oeis.org

6001, 6433, 11085116, 44496481, 96040393, 115916930617, 227007035017, 274101929528, 434985419768, 749978863753, 996004003993, 1365379857457948, 1410590590957816, 1762388551055953, 2307340946901148, 2700383162251217
Offset: 1

Views

Author

Giovanni Resta, Jan 24 2006

Keywords

Comments

Also numbers k such that k concatenated with k+7 gives the product of two numbers which differ by 2.
Also numbers k such that k concatenated with k+4 gives the product of two numbers which differ by 4.
Also numbers k such that k concatenated with k-1 gives the product of two numbers which differ by 6.
Also numbers k such that k concatenated with k-8 gives the product of two numbers which differ by 8.

Examples

			6001//6009 = 7747^2, where // denotes concatenation.
96040393//96040400 = 98000200 * 98000202.
96040393//96040397 = 98000199 * 98000203.
96040393//96040392 = 98000198 * 98000204.

Crossrefs

Cf. A030465, A102567, A115426, A115437, A115428, A115430, A115431, A115432, A115433, A115434, A115435, A115436, A115440.
Cf. A116107, A116109, A116113, A116239.
Cf. A116205, A115430, A116335, A116185, A116187, A116317.
Cf. A116131, A116112, A116152, A116159, A116282.

Extensions

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

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

A116262 n times n+6 gives the concatenation of two numbers m and m-4.

Original entry on oeis.org

42, 53, 38160, 61835, 83615, 346977, 653018, 950048, 8647552, 9534262, 8167822280, 9007920989, 9209900789, 9950000498, 4737445289218, 4990568257184, 5009431742811, 5262554710777, 8373808925582
Offset: 1

Views

Author

Giovanni Resta, Feb 06 2006

Keywords

Crossrefs

Cf. A116131, A116256, A116261, A116263, A116282.

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.

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
Showing 1-5 of 5 results.

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

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