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.

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

Extensions

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

Crossrefs

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

A116113 Numbers k such that k concatenated with k-7 gives the product of two numbers which differ by 8.

Original entry on oeis.org

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

Examples

			8533818720//8533818713 = 9237867023 * 9237867031, where // denotes concatenation.
		

Crossrefs

A116109 Numbers k such that k concatenated with k-8 gives the product of two numbers which differ by 9.

Original entry on oeis.org

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

Examples

			8505429358//8505429350 = 9222488466 * 9222488475, where // denotes concatenation.
		

Crossrefs

A116245 n times n+9 gives the concatenation of two numbers m and m-7.

Original entry on oeis.org

8, 698, 775, 789, 866, 42336, 57656, 96882, 44121665, 55878327, 85298136, 36680703009575609347721358492, 63319296990424390652278641500, 69346342454876071597336150480, 81501115172242572470460459682
Offset: 1

Views

Author

Giovanni Resta, Feb 06 2006

Keywords

Examples

			85298136 * 85298145 = 72757727//72757720, where // denotes
concatenation.
		

Crossrefs

Showing 1-5 of 5 results.