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 1-6 of 6 results.

A115428 Numbers k such that the concatenation of k with k+5 gives a square.

Original entry on oeis.org

1, 4, 20, 31, 14564, 38239, 69919, 120395, 426436, 902596, 7478020, 9090220, 6671332084, 8114264059, 8482227259, 9900250996, 2244338786836, 2490577152964, 2509440638591, 2769448208395, 7012067592220
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 4.
Also numbers k such that k concatenated with k+4 gives the product of two numbers which differ by 2.

Examples

			14564_14569 = 38163^2.

Crossrefs

Cf. A030465, A102567, A115426, A115437, A115429, A115430, A115431, A115432, A115433, A115434, A115435, A115436, A115439.
Cf. A116125, A116099, A116167, A116297, A116177, A116171, A116185, A116315.

Extensions

Edited by N. J. A. Sloane, Apr 13 2007

A116308 Numbers k such that k*(k+2) is the concatenation of two numbers m and m+3.

Original entry on oeis.org

452, 547, 690, 855, 4381, 5618, 72729, 346532, 653467, 9090907, 94117645, 334665332, 336032386, 378253327, 390977441, 439928490, 483516485, 516483514, 560071509, 609022558, 621746672, 663967613, 665334667
Offset: 1

Views

Author

Giovanni Resta, Feb 06 2006

Keywords

Crossrefs

Cf. A116177, A116295, A116307, A116309, A116315.

A116316 Numbers k such that k*(k+3) gives the concatenation of two numbers m and m+4.

Original entry on oeis.org

386, 430, 568, 612, 815, 4522, 5476, 90911, 316833, 683165, 3636365, 6363633, 82352943, 331668333, 368421054, 395604392, 442767755, 461538463, 488721801, 511278197, 538461535, 557232243, 604395606, 631578944, 668331665
Offset: 1

Views

Author

Giovanni Resta, Feb 06 2006

Keywords

Crossrefs

Cf. A116185, A116309, A116315, A116317, A116330.

A116314 Numbers k such that k*(k+1) gives the concatenation of two numbers m and m+4.

Original entry on oeis.org

28, 72, 79822845, 69852478553064869297984899963807, 77473062193002372448027740546439, 77747359197583788609974143907619, 84341826458653210947638195982115, 85367942837521291760016984490251
Offset: 1

Views

Author

Giovanni Resta, Feb 06 2006

Keywords

Examples

			79822845 * 79822846 = 63716866//63716870, where // denotes concatenation.

Crossrefs

Cf. A116171, A116307, A116315, A116322.

A116335 Numbers k such that k*(k+2) gives the concatenation of two numbers m and m+7.

Original entry on oeis.org

7746, 8020, 33294317, 66705682, 98000200, 340465755424, 476452552744, 523547447255, 659534244575, 866013200680, 998000002000, 3695104677080133, 3755782995538767, 4198081170077530, 4803478892324965, 5196521107675034
Offset: 1

Views

Author

Giovanni Resta, Feb 06 2006

Keywords

Examples

			98000200 * 98000202 = 96040393//96040400, where // denotes concatenation.

Crossrefs

Cf. A115429, A116315, A116336, A116344.

A228569 Binomial transform of A006497.

Original entry on oeis.org

2, 5, 19, 80, 343, 1475, 6346, 27305, 117487, 505520, 2175139, 9359135, 40270258, 173273885, 745558651, 3207971600, 13803182047, 59391995435, 255550431034, 1099576168865, 4731229551223, 20357419249520, 87593407593931, 376894780221095, 1621693678323682
Offset: 0

Views

Author

R. J. Mathar, Nov 10 2013

Keywords

Links

Programs

  • Mathematica
    LinearRecurrence[{5,-3},{2,5},30] (* Harvey P. Dale, Sep 09 2017 *)

Formula

G.f.: ( 2-5*x ) / ( 1-5*x+3*x^2 ).
a(n) = 2*A116415(n)-5*A116315(n-1) for n>0.
Showing 1-6 of 6 results.

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

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