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 1-8 of 8 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

A116180 Numbers k such that k concatenated with k+3 gives the product of two numbers which differ by 7.

Original entry on oeis.org

7137, 7767, 47783068991048776635, 48797525371338932241, 55658688122404752991, 56753136503494828605, 85555875266989354735, 86911515887391841491, 95992713077544748491, 97428345698747155255
Offset: 1

Views

Author

Giovanni Resta, Feb 06 2006

Keywords

Comments

Also numbers k such that k concatenated with k-5 gives the product of two numbers which differ by 9.
Also numbers k such that k concatenated with k+9 gives the product of two numbers which differ by 5.

Examples

			7767//7770 = 8810 * 8817, where // denotes concatenation.
7767//7762 = 8809 * 8818.
7767//7776 = 8811 * 8816.

Crossrefs

Cf. A116167, A116179, A116181, A116133, A116311.
Cf. A116114, A116126, A116133, A116258.
Cf. A116207, A116187, A116174, A116351.

Extensions

Edited by N. J. A. Sloane, Apr 12 2007

A116193 Numbers k such that k concatenated with k+5 gives the product of two numbers which differ by 5.

Original entry on oeis.org

11, 45, 18281, 32769, 56891, 180689, 330539, 959481, 1850201, 3247409, 4940219, 2425563239, 2575561739, 6003563495, 7245212645, 7770160145, 4983798265289, 5049762270381, 5534298528989, 5603798594169, 21894082450101
Offset: 1

Views

Author

Giovanni Resta, Feb 06 2006

Keywords

Comments

Also numbers k such that k concatenated with k+9 gives the product of two numbers which differ by 3. For proof that this is the same sequence compare A116133.
Also numbers k such that k concatenated with k-9 gives the product of two numbers which differ by 9.

Examples

			7770160145//7770160136 = 8814851183 * 8814851192, where // denotes concatenation.

Crossrefs

Cf. A116205, A116187, A116349.
Cf. A116179, A115430, A116194, A116200, A116324.
Cf. A116099, A116109, A116231.

Extensions

Edited by N. J. A. Sloane, Apr 12 2007

A116133 Numbers k such that k concatenated with k-4 gives the product of two numbers which differ by 9.

Original entry on oeis.org

64, 1876, 3214, 8776, 17227120144584448354, 19391087990479091186, 21557280540171744040, 23970390649400564404, 26051259424903756364, 28697643366269876506, 31320461807899711990, 34215988012600009664
Offset: 1

Views

Author

Giovanni Resta, Feb 06 2006

Keywords

Comments

Also numbers k such that k concatenated with k+4 gives the product of two numbers which differ by 7.
Since k*(10^j+1) + 4 = m*(m+7) iff k*(10^j+1) - 4 = m*(m+7) - 8 = (m-1)*(m+8) = M*(M+9) this is trivially the same sequence. - N. J. A. Sloane, Apr 11 2007

Examples

			8776//8772 = 9364 * 9373, where // denotes concatenation. Also 8776//8780 = 9365 * 9372.

Crossrefs

Cf. A116132, A116140, A116264.
Cf. A116180, A116187, A116189, A116195, A116319.

Extensions

Edited by N. J. A. Sloane, Apr 11 2007

A116173 Numbers k such that k concatenated with k+2 gives the product of two numbers which differ by 6.

Original entry on oeis.org

6752089, 6448802889351008245, 18894512461523256139943105859903480218905, 31958875438439894736354375209245786214798
Offset: 1

Views

Author

Giovanni Resta, Feb 06 2006

Keywords

Comments

Also numbers k such that k concatenated with k+7 gives the product of two numbers which differ by 4.
If k+2 and k-5 have the same number of digits, the k is also in A116126, because k//k+2 = 10^d*k + k + 2 = m*(m+6) then implies a representation k//k-5 = 10^d*k + k - 5 = m*(m+6)-7 = (m-1)*(m+7). - R. J. Mathar, Aug 10 2008

Examples

			6752089//6752091 = 8217107 * 8217113, where // denotes concatenation.
6752089//6752096 = 8217108 * 8217112.

Crossrefs

Cf. A116159, A116172, A116174, A116187, A116304.
Cf. A115430, A116205, A116207, A116187, A116337.

Extensions

Edited by N. J. A. Sloane, Apr 12 2007

A116194 Numbers k such that k concatenated with k+5 gives the product of two numbers which differ by 6.

Original entry on oeis.org

1, 2, 10, 47, 550, 802, 570035, 623387, 1327222, 4041011, 8252210, 164398539591831062, 173868055738777586, 339918283297349107, 353476744122425611, 846974882088186070, 868300386379144450
Offset: 1

Views

Author

Giovanni Resta, Feb 06 2006

Keywords

Examples

			8252210//8252215 = 9084165 * 9084171, where // denotes
concatenation.

Crossrefs

Cf. A116187, A116193, A116195, A116208, A116325.

A116318 n times n+6 gives the concatenation of two numbers m and m+4.

Original entry on oeis.org

32, 63, 45211540, 54788455, 78317867, 72388446037855609175404257, 73247326752475247326752672, 75267524732673267524732472, 76126405447292905676080887, 42053270820132695893502981749303
Offset: 1

Views

Author

Giovanni Resta, Feb 06 2006

Keywords

Examples

			78317867 * 78317873 = 61336887//61336891, where // denotes
concatenation.

Crossrefs

Cf. A116187, A116304, A116317, A116319, A116325.

A116350 Numbers k such that k*(k+4) gives the concatenation of two numbers m and m+9.

Original entry on oeis.org

33, 64, 45211541, 54788456, 78317868, 72388446037855609175404258, 73247326752475247326752673, 75267524732673267524732473, 76126405447292905676080888, 42053270820132695893502981749304
Offset: 1

Views

Author

Giovanni Resta, Feb 06 2006

Keywords

Examples

			78317868 * 78317872 = 61336887//61336896, where // denotes concatenation.

Crossrefs

Cf. A116187, A116337, A116349, A116351.
Showing 1-8 of 8 results.

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

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