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.

A087240 First differences of A087235.

Original entry on oeis.org

25, 87, 240, 774, 1960, 5378, 15828, 40420, 110477, 306255, 823267, 2219935, 6035446, 16314684, 44245201, 119849369, 324308909, 879921037, 2385657333, 6467079803, 17541637367, 47581552613, 129104928784, 350330765356, 950772205549, 2580621276899, 7005302330033
Offset: 2

Views

Author

Labos Elemer, Sep 04 2003

Keywords

Crossrefs

Formula

a(n)=A087235(n+1)-A087235(n)

Extensions

More terms from Giovanni Resta, Sep 01 2018

A256394 Prime values of pi(n) that divide n.

Original entry on oeis.org

2, 3, 11, 67, 71, 439, 1051, 6469, 40087, 100361, 100363, 251737, 251761, 637319, 637327, 4124459, 10553513, 10553551, 27067277, 69709733, 179993171, 465769817, 3140421769, 8179002109, 8179002133, 55762149029, 55762149071, 382465573489, 1003652347081
Offset: 1

Views

Author

Jonathan Sondow, Apr 13 2015

Keywords

Comments

a(n) is the largest prime factor of n, since pi(n) ~ n / log n.

Examples

			pi(6) = 3 is prime, and 3 divides 6, so 3 is a member.
		

Crossrefs

Programs

  • Mathematica
    c = 0; lpf[n_] := If[ PrimeQ[n], c++; n, Transpose[ FactorInteger[n]][[1, -1]]]; Do[ If[lpf[n] == c, Print[ PrimePi[n]]], {n, 2, 10^7}]
    PrimePi[Select[Select[Range[2,10^6],IntegerQ[#/PrimePi[#]]&],PrimeQ[PrimePi[#]]&]] (* Ivan N. Ianakiev, Apr 15 2015 *)
    Select[Table[{PrimePi[n],n},{n,10^6}],PrimeQ[#[[1]]]&&Divisible[#[[2]],#[[1]]]&][[All,1]] (* The program generates the first 9 terms of the sequence. To generate more, increase the constant for n. *) (* Harvey P. Dale, Feb 08 2022 *)
  • PARI
    for(n=1,10^6,if(isprime(p=primepi(n))&&!(n%primepi(n)),print1(p,", "))) \\ Derek Orr, Apr 14 2015

Formula

a(n) = A000720(A071394(n)) = A006530(A071394(n)).

Extensions

More terms from Giovanni Resta, Sep 01 2018

A087239 First differences of A038625.

Original entry on oeis.org

25, 69, 234, 678, 2051, 5349, 15118, 41014, 110657, 305655, 823646, 2219386, 6034071, 16316797, 44240660, 119845770, 324311229, 879921169, 2385656018, 6467086046, 17541630385, 47581555131, 129104931215, 350330768077, 950772203169, 2580621278375, 7005302328953
Offset: 2

Views

Author

Labos Elemer, Sep 04 2003

Keywords

Crossrefs

Formula

a(n)=A038625(n+1)-A038625(n)

Extensions

More terms from Giovanni Resta, Sep 01 2018
Showing 1-3 of 3 results.