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 1-3 of 3 results.

A232746 n occurs A030124(n) times; a(n) = one less than the least k such that A005228(k) > n.

Original entry on oeis.org

1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10
Offset: 1

Views

Author

Antti Karttunen, Nov 30 2013

Keywords

Comments

The characteristic function for Hofstadter's A005228 is given by X_A005228(1)=1, and for n>1, X_A005228(n) = a(n)-a(n-1).
The characteristic function for Hofstadter's A030124 is given by X_A030124(1)=0, and for n>1, X_A030124(n) = 1-(a(n)-a(n-1)).
Useful when computing A232747, A232748, A232750 & A225850.

Links

Crossrefs

Cf. A005228, A030124, A232747, A232748, A232750, A232753, A225850.

Programs

  • Mathematica
    nmax = 100; A5228 = {1}; Module[{d = 2, k = 1}, Do[While[MemberQ[A5228, d], d++]; k += d; d++; AppendTo[A5228, k], {n, 1, nmax}]];
a[n_] := For[k = 1, True, k++, If[A5228[[k]] > n, Return[k-1]]];
Array[a, nmax] (* Jean-François Alcover, Dec 09 2021 *)

Formula

a(n) = one less than the least k such that A005228(k) > n.

A242752 Primes p such that pi(p) is a primitive root modulo p, where pi(p) is the number of primes not exceeding p.

Original entry on oeis.org

2, 3, 5, 13, 17, 29, 31, 41, 47, 61, 89, 101, 107, 137, 167, 179, 193, 197, 223, 229, 251, 257, 263, 271, 293, 313, 337, 347, 353, 379, 401, 431, 439, 487, 499, 587, 593, 599, 601, 643, 647, 653, 659, 677, 701, 727, 733, 739, 751, 797, 821, 823, 829, 857, 919, 929, 941, 967, 971, 983
Offset: 1

Views

Author

Zhi-Wei Sun, May 21 2014

Keywords

Comments

According to the conjecture in A232748, this sequence should contain infinitely many primes.

Examples

			a(3) = 5 since 5 is prime with pi(5) = 3 a primitive root modulo 5.

Links

Crossrefs

Cf. A000040, A000720, A242748, A242750.

Programs

  • Mathematica
    dv[n_]:=Divisors[n]
n=0;Do[Do[If[Mod[k^(Part[dv[Prime[k]-1],j]),Prime[k]]==1,Goto[aa]],{j,1,Length[dv[Prime[k]-1]]-1}];n=n+1;Print[n," ",Prime[k]];Label[aa];Continue,{k,1,166}]

A232749 Inverse function to Hofstadter's A030124.

Original entry on oeis.org

0, 1, 0, 2, 3, 4, 0, 5, 6, 7, 8, 0, 9, 10, 11, 12, 13, 0, 14, 15, 16, 17, 18, 19, 20, 0, 21, 22, 23, 24, 25, 26, 27, 28, 0, 29, 30, 31, 32, 33, 34, 35, 36, 37, 0, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 0, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 0, 60
Offset: 1

Views

Author

Antti Karttunen, Nov 30 2013

Keywords

Comments

This is an inverse function for Hofstadter's A030124 in the sense that for all n, n = a(A030124(n)). a(n) = 0 when n is not in A030124, but instead in its complement A005228.
Note that A232747(n)*a(n) = 0 for all n.
Used to compute the permutation A232751.

Links

Crossrefs

A005228 gives the positions of zeros.
Cf. A030124, A232747, A232748, A232751.

Programs

  • Mathematica
    nmax = 100; A5228 = {1};
Module[{d = 2, k = 1}, Do[While[MemberQ[A5228, d], d++];
     k += d; d++; AppendTo[A5228, k], {n, 1, nmax}]];
a46[n_] := For[k = 1, True, k++, If[A5228[[k]] > n, Return[k - 1]]];
a48[n_] := a48[n] = If[n == 1, 0, a48[n-1] + (1 - (a46[n] - a46[n - 1]))];
a[n_] := If[n == 1, 0, a48[n] (a48[n] - a48[n - 1])];
Array[a, nmax] (* Jean-François Alcover, Dec 09 2021 *)
Showing 1-3 of 3 results.

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