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.

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A126882 a(1)=2. a(n) is the a(n-1)st integer from among those positive integers coprime to a(n-1).

Original entry on oeis.org

2, 3, 4, 7, 8, 15, 28, 65, 87, 134, 271, 272, 577, 578, 1227, 1844, 3695, 4624, 9825, 18562, 37127, 37537, 37538, 75627, 113480, 283799, 283800, 1198543, 1201967, 1302144, 3907583, 3907584, 11948189, 13143019, 13151298, 39453911, 46029570
Offset: 1

Views

Author

Leroy Quet, Dec 29 2006

Keywords

Examples

			a(4)=7. So a(5) is the 7th positive integer which is coprime to 7. 7 is coprime to 1,2,3,4,5,6,8,9,10,... So a(5) is the 7th of these, which is 8.

Crossrefs

Cf. A069213, A126881.

Programs

  • Mathematica
    f[n_] := Block[{k = 0, c = n},While[c > 0,k++;While[GCD[k, n] > 1, k++ ];c--;];k];g[l_] := Append[l, f[l[[ -1]]]];Nest[g, {2}, 36] (* Ray Chandler, Dec 31 2006 *)

Formula

a(n) = A069213(a(n-1)).

Extensions

Extended by Ray Chandler, Dec 31 2006

A130700 a(0)=1; a(n) is the n-th integer from among those positive integers which are coprime to (a(n-1)*n).

Original entry on oeis.org

1, 1, 3, 4, 7, 6, 17, 8, 15, 16, 23, 12, 35, 19, 33, 31, 33, 29, 55, 27, 73, 37, 49, 27, 71, 31, 57, 43, 67, 30, 109, 32, 63, 64, 71, 51, 113, 38, 79, 62, 103, 42, 145, 56, 111, 88, 105, 106, 145, 73, 127
Offset: 0

Views

Author

Leroy Quet, Aug 12 2007

Keywords

Examples

			a(8)*9 = 135. Those positive integers which are coprime to 135 form the sequence: 1,2,4,7,8,11,13,14,16,17,19,22,... The 9th of these integers is 16, so a(9) = 16.

Links

Crossrefs

Cf. A069213.

Programs

  • Maple
    a[0]:=1: for n to 50 do CP:={}: for j while nops(CP)<=n do if gcd(n*a[n-1],j) =1 then CP:=`union`(CP,{j}) else end if end do: a[n]:=CP[n] end do: seq(a[n], n=0..50); # Emeric Deutsch, Aug 28 2007

Extensions

More terms from Emeric Deutsch, Aug 28 2007

A131504 Array read by antidiagonals: a(m,n) = m-th integer from among those positive integers that are coprime to (m*n).

Original entry on oeis.org

1, 1, 3, 1, 3, 4, 1, 5, 7, 7, 1, 3, 4, 7, 6, 1, 3, 7, 11, 11, 17, 1, 5, 4, 7, 8, 17, 8, 1, 3, 7, 9, 11, 17, 15, 15, 1, 3, 4, 11, 6, 17, 11, 15, 13, 1, 5, 7, 9, 17, 19, 15, 23, 25, 23, 1, 3, 4, 7, 6, 17, 9, 15, 13, 23, 12, 1, 3, 11, 11, 11, 19, 23, 19, 25, 37, 23, 35, 1, 5, 4, 9, 8, 17, 8, 23, 16
Offset: 1

Views

Author

Leroy Quet, Aug 13 2007

Keywords

Examples

			For example:
a(6,5) = 19 because the positive integers which are coprime to (5*6) are 1,7,11,13,17,19,23,29,... and the 6th of these is 19.
Array begins:
1, 3, 4, 7, 6,17, 8,15,13,23,12,35,14,...
1, 3, 7, 7,11,17,15,15,25,23,23,35,27,...
1, 5, 4,11, 8,17,11,23,13,37,17,35,20,...
1, 3, 7, 7,11,17,15,15,25,23,23,35,27,...
1, 3, 4, 9, 6,19, 9,19,16,23,14,43,17,...
1, 5, 7,11,17,17,23,23,25,37,35,35,41,...
1, 3, 4, 9, 6,19, 8,17,16,29,13,41,16,...
1, 3, 7, 7,11,17,15,15,25,23,23,35,27,...
1, 5, 4,11, 8,17,11,23,13,37,17,35,20,...
1, 3,11, 9,11,19,19,19,31,23,29,43,33,...
1, 3, 4, 7, 6,19, 8,17,14,27,12,37,15,...
1, 5, 7,11,17,17,23,23,25,37,35,35,41,...

Crossrefs

Cf. A069213.

Programs

  • Maple
    A131504 := proc(n,m) local mn,a,k ; mn := m*n ; k := 1; for a from 1 do if gcd(a,mn) = 1 then if k = m then RETURN(a) ; fi ; k := k+1 ; fi ; od: end: for d from 1 to 14 do for m from 1 to d do printf("%d,",A131504(d+1-m,m)) ; od: od: # R. J. Mathar, Oct 26 2007

Extensions

More terms from R. J. Mathar, Oct 26 2007

A121274 a(n) = n-th integer from among those positive integers which are coprime to (n-th integer from among those positive integers which are coprime to n).

Original entry on oeis.org

1, 2, 5, 4, 13, 6, 13, 14, 9, 10, 31, 17, 29, 14, 33, 16, 49, 18, 47, 23, 21, 22, 67, 24, 25, 36, 67, 37, 107, 30, 61, 55, 33, 34, 55, 36, 77, 38, 79, 65, 143, 53, 93, 58, 45, 61, 139, 57, 77, 76, 127, 80, 157, 65, 113, 85, 57, 72, 221, 60, 125, 62, 63, 64, 100, 79, 141, 81
Offset: 1

Views

Author

Leroy Quet, Aug 23 2006

Keywords

Examples

			6 is the 5th positive integer which is coprime to 5. (1,2,3,4,6,7,8.... is the sequence of positive integers which are coprime to 5 and 6 is the 5th such integer.) 1,5,7,11,13,17,19,... are the positive integers which are coprime to 6. 13 is the 5th of these integers, so a(5) = 13.

Crossrefs

Cf. A069213.

Extensions

Extended by Ray Chandler, Aug 29 2006

A123279 a(n) = product of the first n integers from among those positive integers which are coprime to n.

Original entry on oeis.org

1, 3, 8, 105, 144, 85085, 5760, 2027025, 3203200, 4216455243, 43545600, 29248404810625, 6706022400, 1305433904506875, 1707444076642304, 191898783962510625, 376610217984000, 232876694951587194633125
Offset: 1

Views

Author

Leroy Quet, Dec 11 2006

Keywords

Examples

			The first 4 positive integers which are coprime to 4 are 1,3,5,7. So a(4) = 1*3*5*7 = 105.

Crossrefs

Cf. A069213, A077581, A077582.

Programs

  • Mathematica
    f[n_] := Block[{c = n, k = 0, p = 1},While[c > 0,k++;While[GCD[k, n] > 1, k++ ];c--;p *= k;];p];Table[f[n], {n, 20}] (* Ray Chandler, Dec 14 2006 *)

Extensions

Extended by Ray Chandler, Dec 14 2006

A139766 A number n is included in the sequence if and only if the n-th integer from among those positive integers which are coprime to n+1 = the (n+1)-st integer from among those positive integers which are coprime to n.

Original entry on oeis.org

3, 15, 104, 164, 255, 2625, 2834, 11715, 18315, 48704, 49215, 64004, 65535, 73124, 131144, 215775, 491535, 525986, 546272, 568815, 952575, 1925564, 5781434, 5861583, 13496384, 14409548, 17646615, 17949434, 20171384, 21475124, 22632285
Offset: 1

Views

Author

Leroy Quet, Nov 07 2007

Keywords

Comments

So far it appears that this is a proper subset of A001274.

Crossrefs

Cf. A001274, A069213, A126356, A126357.

Formula

Indices n such that A126356(n) = A126357(n). - Ray Chandler

Extensions

More terms from Stefan Steinerberger, Nov 07 2007
a(8) onwards from Ray Chandler, Jul 01 2009
Previous Showing 11-16 of 16 results.

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