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 1-10 of 12 results. Next

A075003 Floor[ concatenation of n+1 and n divided by 2 ].

Original entry on oeis.org

5, 10, 16, 21, 27, 32, 38, 43, 49, 54, 555, 605, 656, 706, 757, 807, 858, 908, 959, 1009, 1060, 1110, 1161, 1211, 1262, 1312, 1363, 1413, 1464, 1514, 1565, 1615, 1666, 1716, 1767, 1817, 1868, 1918, 1969, 2019, 2070, 2120, 2171, 2221, 2272, 2322, 2373, 2423
Offset: 0

Views

Author

Amarnath Murthy, Sep 01 2002

Keywords

Examples

			Sequence exhibits similar properties to A074993.

Crossrefs

Cf. A074991 to A075000 and A075004 to A075010.

Programs

  • Maple
    seq(floor((n*10+(n-1))/2),n=1..10),seq(floor((n*100+(n-1))/2),n=11..99);

Extensions

More terms from Sascha Kurz, Jan 14 2003

A075010 a(n) = floor( concatenation of 9 numbers from n+8 to n in that order divided by 9 ).

Original entry on oeis.org

97393690, 109739369, 122085048, 1234430727, 13456776406, 145790122085, 1570134567764, 16823680123443, 179460145790122, 1906834903467901, 20190683490346790, 21313017946014579, 22435352401682368, 23557686857350157, 24680021313017946, 25802355768685735
Offset: 0

Views

Author

Amarnath Murthy, Sep 01 2002

Keywords

Crossrefs

Cf. A074991 to A075000, A075003 to A075009.

Programs

  • Mathematica
    Table[Floor[FromDigits[Flatten[IntegerDigits/@Range[n+8,n,-1]]]/9],{n,0,20}] (* Harvey P. Dale, Aug 04 2019 *)

Extensions

More terms from Sascha Kurz, Jan 14 2003
Corrected and extended by Harvey P. Dale, Aug 04 2019

A075001 Smallest k such that the concatenation of n consecutive numbers starting with k (from k to n+k-1) is a multiple of n; or 0 if no such number exists.

Original entry on oeis.org

1, 1, 1, 3, 1, 1, 3, 5, 1, 1, 9, 1, 4, 7, 1, 5, 23, 1, 14, 1, 9, 9, 13, 5, 1, 21, 1, 13, 12, 1, 36, 21, 9, 3, 41, 1, 34, 33, 9, 21, 12, 9, 33, 9, 1, 13, 28, 5, 48, 1, 23, 21, 3, 1, 11, 13, 14, 41, 28, 1, 114, 115, 9, 41, 21, 9, 23, 69, 1, 61, 73, 5, 14, 43, 1, 145, 13, 9, 127, 41, 9, 95
Offset: 1

Views

Author

Amarnath Murthy, Aug 31 2002

Keywords

Comments

Conjecture: For every n there exists a k.
First occurrence of k where a(n)=k: 1, 103, 4, 13, 8, 105, 14, 87, 11, 699, 55, 29, 23, 19, 114, 261, 102, 97, 178, 219, 26, 121, 17, 151, 92, ..., . - Robert G. Wilson v
a(n)=1 iff n is in A029455. - Robert G. Wilson v
Increasing a(n)'s: 1, 3, 5, 9, 23, 36, 41, 48, 114, 115, 145, 166, 175, 221, 251, ..., at n = 1, 4, 8, 11, 17, 31, 35, 49, 61, 62, 76, 85, 122, 133, 170, 179, 217, 229, ..., . - Robert G. Wilson v

Examples

			a(11) = 9 as 910111213141516171819 the concatenation of 11 numbers from 9 to 19 is divisible by 11 (11*82737383012865106529).

Links

Crossrefs

Cf. A058183, A074991, A074992, A074993, A074994, A074995, A074996, A036377, A073086, A074999, A075000, A077306, A075000.
Cf. A029455 (indices of 1's).

Programs

  • Mathematica
    f[n_] := Block[{c = 1, id = Range@n}, While[k = FromDigits@Flatten@IntegerDigits@id/n; ! IntegerQ@k, id++; c++ ]; c]; Array[f, 82] (* Robert G. Wilson v, Oct 20 2007 *)
  • PARI
    /* The following program assumes the conjecture is true. */ /* It has found nonzero a(n) for n up to 500. */ {for(n=1,500, k=0; until(s%n==0,k++; s=0; for(m=k,k+n-1, s=s*(10^length(Str(m)))+m)); print1(k,","))}
  • PARI
    a(n) = {my(ld = 1, hd = n, qd, m = Mod(1, n), pow10, qdn = #digits(n), t=log(10*n+.5)\log(10)); qd = n*t+t-10^t\9; pow10 = Mod(10, n)^(qd-1); for(i = 2, n, m = m * Mod(10, n)^#digits(i) + i; ); while(1, if(lift(m) == 0, return(ld)); m -= ld * pow10; hd++; m = m * Mod(10, n)^#digits(hd) + hd; ld++; pow10*=10^(#digits(hd) - #digits(ld)); ) } \\ David A. Corneth, Aug 23 2020

Extensions

More terms from Rick L. Shepherd, Sep 03 2002

A077306 Smallest multiple of n formed by the concatenation of n successive numbers, or 0 if no such number exists.

Original entry on oeis.org

1, 12, 123, 3456, 12345, 123456, 3456789, 56789101112, 123456789, 12345678910, 910111213141516171819, 123456789101112, 45678910111213141516, 7891011121314151617181920, 123456789101112131415, 567891011121314151617181920
Offset: 1

Views

Author

Amarnath Murthy, Nov 03 2002

Keywords

Links

Crossrefs

Cf. A075000, A077308.

Programs

  • Maple
    digs := proc(inp::integer) local resul,shiftinp : resul := 1 : shiftinp := iquo(inp,10) : while shiftinp > 0 do resul := resul+1 : shiftinp := iquo(shiftinp,10) : od : RETURN(resul) : end: # provide number of concatenation of frst up to lst newnum := proc(frst::integer,lst::integer) local resul,i : resul:= frst : for i from frst+1 to lst do resul := resul*10^digs(i)+i : od : RETURN(resul) ; end : n := 1 : while n < 20 do nold := n : newfeedstrt := 1 : newfeedend := newfeedstrt + n-1 : while nold = n do trythis := newnum(newfeedstrt,newfeedend) : if ( trythis mod n ) = 0 then printf("%a,",trythis) ; n := n+ 1: break : fi : newfeedstrt := newfeedstrt + 1 : newfeedend := newfeedstrt + n-1 : od : od : # R. J. Mathar, Mar 13 2006
  • Mathematica
    a[n_] := Block[{v, k = 1}, While[Mod[v = FromDigits@ Flatten@ IntegerDigits@ Range[k, k+n-1], n] > 0, k++]; v]; Array[a,20] (* Giovanni Resta, May 12 2013 *)

Extensions

More terms from R. J. Mathar, Mar 13 2006

A075004 Floor[ concatenation of n+2, n+1 and n divided by 3 ].

Original entry on oeis.org

70, 107, 144, 181, 218, 255, 292, 329, 366, 3703, 40370, 43737, 47104, 50471, 53838, 57205, 60572, 63939, 67306, 70673, 74040, 77407, 80774, 84141, 87508, 90875, 94242, 97609, 100976, 104343, 107710, 111077, 114444, 117811, 121178, 124545
Offset: 0

Views

Author

Amarnath Murthy, Sep 01 2002

Keywords

Examples

			Sequence exhibits similar properties to A074991.

Crossrefs

Cf. A074991 to A075000, A075003 and A075005 to A075010.

Programs

  • Maple
    70, 107, 144, 181, 218, 255, 292, 329, 366, 3703, seq(floor(((n+2)*10^4+(n+1)*10^2+n)/3),n=10..99);

Extensions

More terms from Sascha Kurz, Jan 14 2003

A075005 Floor[ concatenation of n+3, n+2, n+1 and n divided by 4 ].

Original entry on oeis.org

802, 1080, 1358, 1635, 1913, 2191, 2469, 2746, 27774, 302777, 3280277, 3532802, 3785328, 4037853, 4290378, 4542903, 4795429, 5047954, 5300479, 5553004, 5805530, 6058055, 6310580, 6563105, 6815631, 7068156, 7320681, 7573206
Offset: 0

Views

Author

Amarnath Murthy, Sep 01 2002

Keywords

Crossrefs

Cf. A074991 to A075000, A075003, A075004 and A074996 to A075010.

Programs

  • Maple
    seq(floor(((n+3)*1000+(n+2)*100+(n+1)*10+n)/4), n=0..7), floor(111098/4), floor(1211109/4), seq(floor(((n+3)*1000^2+(n+2)*100^2+(n+1)*10^2+n)/4), n=10..99);

Extensions

More terms from Sascha Kurz, Jan 14 2003

A075007 a(n) = floor(concatenation of n+5, n+4, n+3, n+2, n+1 and n divided by 6).

Original entry on oeis.org

90535, 109053, 127572, 146090, 164609, 183127, 1851646, 20185164, 218685183, 2355201851, 25235520185, 26919021868, 28602523552, 30286025235, 31969526919, 33653028602, 35336530286, 37020031969, 38703533653, 40387035336
Offset: 0

Views

Author

Amarnath Murthy, Sep 01 2002

Keywords

Links

Crossrefs

Cf. A074991 to A075000, A075003 to A075006 and A073086 to A075010.

Programs

  • Maple
    f:= proc(n) local i; floor(parse(cat(seq(i,i=n+5 .. n, -1)))/6) end proc:
map(f, [$0..40]); # Robert Israel, Jan 11 2024
  • Mathematica
    fc[n_]:=Module[{c=Reverse[n]},Floor[FromDigits[Flatten[IntegerDigits/@ c]]/ 6]]; fc/@Partition[Range[0,30],6,1] (* Harvey P. Dale, Nov 09 2014 *)

Extensions

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 18 2003

A075008 Floor[ concatenation of 7 numbers from n+6 to n in that order divided by 7].

Original entry on oeis.org

934744, 1093474, 1252204, 1410934, 1569664, 15871252, 173015696, 1874444426, 20187444442, 216304458729, 2307344731587, 2451644875887, 2595945020187, 2740245164487, 2884545308787, 3028845453087, 3173145597388, 3317445741688
Offset: 0

Views

Author

Amarnath Murthy, Sep 01 2002

Keywords

Links

Crossrefs

Cf. A074991 to A075000, A075003 to A075007, A074999, A075010.

Programs

  • Mathematica
    Table[Floor[FromDigits[Flatten[IntegerDigits/@Range[n+6,n,-1]]]/7],{n,0,20}] (* Harvey P. Dale, May 20 2021 *)

Extensions

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 18 2003

A075009 Floor[ concatenation of 8 numbers from n+7 to n in that order divided by 8].

Original entry on oeis.org

9567901, 10956790, 12345679, 13734567, 138873456, 1513887345, 16401388734, 176640138873, 1892664013887, 20189266401388, 214518926640138, 227145189266401, 239771451892664, 252397714518926, 265023977145189
Offset: 0

Views

Author

Amarnath Murthy, Sep 01 2002

Keywords

Links

Crossrefs

Cf. A074991 to A075000, A075003 to A075008, A075010.

Programs

  • Mathematica
    Table[Floor[FromDigits[Flatten[IntegerDigits/@Range[n,n-7,-1]]]/8], {n,7,30}] (* Harvey P. Dale, Feb 14 2016 *)

Extensions

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 18 2003

A075006 Floor[ concatenation of n+4, n+3, n+2, n+1 and n divided by 5].

Original entry on oeis.org

8642, 10864, 13086, 15308, 17530, 19753, 21975, 222197, 2422219, 26242221, 282624222, 302826242, 323028262, 343230282, 363432302, 383634323, 403836343, 424038363, 444240383, 464442403, 484644424, 504846444, 525048464, 545250484
Offset: 0

Views

Author

Amarnath Murthy, Sep 01 2002

Keywords

Crossrefs

Cf. A074991 to A075000, A075003 to A075005 and A036377 to A075010.

Extensions

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 18 2003
Showing 1-10 of 12 results. Next

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