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 1-9 of 9 results.

A115430 Numbers k such that the concatenation of k with k+9 gives a square.

Original entry on oeis.org

216, 287, 515, 675, 1175, 4320, 82640, 960795, 1322312, 4049591, 16955015, 34602080, 171010235, 181964891, 183673467, 187160072, 321920055, 326530616, 328818032, 343942560, 470954312, 526023432, 528925616, 534830855
Offset: 1

Views

Author

Giovanni Resta, Jan 24 2006

Keywords

Comments

Also numbers k such that k concatenated with k+8 gives the product of two numbers which differ by 2.
Also numbers k such that k concatenated with k+5 gives the product of two numbers which differ by 4.

Examples

			82640_82649 = 90907^2.

Crossrefs

Cf. A030465, A102567, A115426, A115437, A115428, A115429, A115431, A115432, A115433, A115434, A115435, A115436, A115441.
Cf. A116172, A116168, A116344, A116112, A116193, A116173, A116323.

Extensions

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

A116205 Numbers k such that k concatenated with k+7 gives the product of two numbers which differ by 3.

Original entry on oeis.org

1, 81, 1353, 3997, 7723, 23761, 26271, 76771, 1415683, 3890571, 8495497, 1066870443, 1239366513, 4198438981, 4534273891, 6502317141, 6918679731, 2199164200036329043, 2820114781174460091, 5500888421709400741
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 1.
Also numbers k such that k concatenated with k-3 gives the product of two numbers which differ by 7.

Crossrefs

Cf. A116179, A116172, A115429, A116173, A116193, A116336.
Cf. A116132, A116099, A116139, A116152, A116269, A116348.

Extensions

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

A116174 Numbers k such that k concatenated with k+2 gives the product of two numbers which differ by 8.

Original entry on oeis.org

1143, 4382, 4943, 24941511, 25058558, 94090583, 616729341438, 638432642423, 978717194478, 994009005983, 1636200161363007, 1710661666314798, 1805005185949007, 1906479843038783, 1986790648039982, 3072104679280383
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 6.

Examples

			94090583//94090585 = 97000297 * 97000305, where // denotes concatenation.
94090583//94090592 = 97000298 * 97000304.

Crossrefs

Cf. A116168, A116173, A116175, A116181, A116305.
Cf. A116180, A116169, A116352.

Extensions

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

A116187 Numbers k such that k concatenated with k+4 gives the product of two numbers which differ by 6.

Original entry on oeis.org

12, 43, 20440836, 30017751, 61336887, 52400871197755334426147587, 53651708763838760619655612, 56652002793835820319625612, 57952296063256269823192087, 17684775866714240650923831481623
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 4. For proof that this is the same sequence compare A116133.

Examples

			61336887//61336891 = 78317867 * 78317873, where // denotes concatenation. 61336887//61336896 = 78317868 * 78317872.

Crossrefs

Cf. A116173, A115429, A116133, A116194, A116318.
Cf. A116193, A116180, A116350.

Extensions

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

A116207 Numbers k such that k concatenated with k+7 gives the product of two numbers which differ by 5.

Original entry on oeis.org

493, 607, 629, 757, 17927, 33247, 93869, 19467217, 31223879, 72757727, 13454739732766891651472740499, 40093333713615672956030023507, 48089152118689474641229584727, 66424317743191484432891678269
Offset: 1

Views

Author

Giovanni Resta, Feb 06 2006

Keywords

Comments

From Robert Israel, Nov 27 2024: (Start)
If 10^d + 1 has a prime factor p such that 53 is not a square mod p, then there are no terms k where k + 7 has d digits.
For example, there are no terms where d == 2 (mod 4), since in that case 10^d + 1 is divisible by 101, and 53 is not a square mod 101. (End)

Examples

			72757727//72757734 = 85298138 * 85298143, where // denotes concatenation.

Links

Crossrefs

Cf. A116167, A116114, A116200, A116173, A116208, A116180, A116338.

Programs

  • Maple
    f:= proc(d) # terms where k+7 has d digits
    local S,x,R,k;
    S:= map(t -> rhs(op(t)), [msolve(x*(x+5) = 7, 10^d+1)]);
    R:= NULL:
    for x in S do
      k := (x*(x+5)-7)/(10^d+1);
      if ilog10(k+7) = d - 1 then R:= R,k fi
    od:
    op(sort([R]))
end proc:
map(f, [$1..31]); # Robert Israel, Nov 27 2024

A116304 Numbers k such that k*(k+6) gives the concatenation of two numbers m and m+2.

Original entry on oeis.org

8217107, 8030443878983905981, 43467818511541680701794365325328847002051, 56532181488458319298205634674671152997944
Offset: 1

Views

Author

Giovanni Resta, Feb 06 2006

Keywords

Examples

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

Crossrefs

Cf. A116173, A116290, A116303, A116305, A116318.

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.

A116337 Numbers k such that k*(k+4) gives the concatenation of two numbers m and m+7.

Original entry on oeis.org

8217108, 8030443878983905982, 43467818511541680701794365325328847002052, 56532181488458319298205634674671152997945
Offset: 1

Views

Author

Giovanni Resta, Feb 06 2006

Keywords

Examples

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

Crossrefs

Cf. A116173, A116323, A116336, A116338, A116350.
Cf. A116304, A116257.
Showing 1-9 of 9 results.

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

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