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

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

A116168 Numbers k such that k concatenated with k+1 gives the product of two numbers which differ by 8.

Original entry on oeis.org

19, 32, 16284704, 35576083, 15764836187996024260119639732979, 19807200907254352332962649366152, 20298517078413563250826300137112, 30190765850423053042937262322867, 30796637697589506772859224996627
Offset: 1

Views

Author

Giovanni Resta, Feb 06 2006

Keywords

Comments

Also numbers k such that k concatenated with k+8 gives the product of two numbers which differ by 6.

Examples

			35576083//35576084 = 59645686 * 59645694, where // denotes concatenation.
35576083//35576091 = 59645687 * 59645693.

Crossrefs

Cf. A116161, A116167, A116169, A116174, A116299.
Cf. A116208, A115430, A116215, A116345.

Extensions

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

A116160 Numbers k such that k concatenated with itself gives the product of two numbers which differ by 7.

Original entry on oeis.org

4, 94, 210, 294, 994, 5880, 9994, 52888, 99994, 127044, 414180, 999994, 8264470, 9999994, 12456750, 41868508, 99999994, 112670544, 441341880, 468144040, 669421494, 702338994, 715976338, 750005718, 960645294, 999999994
Offset: 1

Views

Author

Giovanni Resta, Feb 06 2006

Keywords

Crossrefs

Cf. A020338, A116152, A116159, A116161, A116167, A116291.

A116298 n times n+7 gives the concatenation of two numbers m and m+1.

Original entry on oeis.org

6, 699, 776, 790, 867, 42337, 57657, 96883, 44121666, 55878328, 85298137, 36680703009575609347721358493, 63319296990424390652278641501, 69346342454876071597336150481, 81501115172242572470460459683
Offset: 1

Views

Author

Giovanni Resta, Feb 06 2006

Keywords

Examples

			85298137 * 85298144 = 72757727//72757728, where // denotes
concatenation.

Crossrefs

Cf. A116167, A116291, A116297, A116299, A116311.
Showing 1-6 of 6 results.

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

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