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.

User: Jianglin Luo

Jianglin Luo's wiki page.

Jianglin Luo has authored 2 sequences.

A385124 Numbers k such that there are exactly 7 primes between 30*k and 30*k+30.

Original entry on oeis.org

1, 2, 49, 62, 79, 89, 188, 6627, 9491, 18674, 22621, 31982, 34083, 38226, 38520, 41545, 48713, 53887, 89459, 103205, 114731, 123306, 139742, 140609, 149125, 168237, 175125, 210554, 223949, 229269, 237794, 240007, 267356, 288467, 321451, 364921, 368248, 373370, 391701
Offset: 1

Views

Author

Jianglin Luo, Jun 18 2025

Keywords

Comments

The count of primes in 30*k..30*k+30 is less than 8 for k >= 1.
It appears that this sequence has infinitely many terms.

Examples

			1 is a term since there are 7 primes in 30..60: 31, 37, 41, 43, 47, 53, 59.
2 is a term since there are 7 primes in 60..90: 61, 67, 71, 73, 79, 83, 89.
3 is not a term since there are only 6 primes in 90..120: 97, 101, 103, 107, 109, 113.
49 is a term since there are 7 primes in 30*49..30*50: 1471, 1481, 1483, 1487, 1489, 1493, 1499.

Links

Crossrefs

Union of A100418, A100419, A100420, A100421, A100422 and A100423.
Cf. A000720, A098592.

Programs

  • Mathematica
    ArrayPlot[Table[Boole@PrimeQ[i*30+j],{i,0,399},{j,30}],Mesh->True]
index=1;Do[If[Length@(*PrimeRange=*) Select[Range[30*k+1,30*k+30,2],PrimeQ]==7,Print[index++," ",k]],{k,1,10^9}]
  • PARI
    [n|n<-[1..10^6],#primes([30*n,30*n+30])==7]

Formula

{k | A098592(k) = pi(30*k+30) - pi(30*k) = 7}. - Michael S. Branicky, Jun 24 2025

A365521 a(1) = 1; for n > 1, a(n) is the prime factor of n that has not appeared for the longest time in {a(1),...,a(n-2),a(n-1)}.

Original entry on oeis.org

1, 2, 3, 2, 5, 3, 7, 2, 3, 5, 11, 2, 13, 7, 3, 2, 17, 3, 19, 5, 7, 11, 23, 2, 5, 13, 3, 7, 29, 2, 31, 2, 11, 17, 5, 3, 37, 19, 13, 2, 41, 7, 43, 11, 5, 23, 47, 3, 7, 2, 17, 13, 53, 3, 11, 7, 19, 29, 59, 5, 61, 31, 3, 2, 13, 11, 67, 17, 23, 7, 71, 3, 73, 37, 5, 19
Offset: 1

Views

Author

Jianglin Luo, Sep 08 2023

Keywords

Examples

			a(6)=3 because 6 = 2*3 and 2=a(4) has appeared more recently than 3=a(3).
a(12)=2 because 12 = 2^2*3 and 3=a(9) has appeared more recently than 2=a(8).
a(30)=2 because 30 = 2*3*5 and 3=a(27) and 5=a(25) have appeared more recently than 2=a(24).

Links

Crossrefs

Cf. A088387, A006530, A034699, A088388.

Programs

  • PARI
    See PARI link \\ David A. Corneth, Sep 08 2023
  • SageMath
    def hpf_seq(top):
    H=[0,1,2,3]
    for n in range(4,top):
        prime_factors=[part[0] for part in list(factor(n))]
        cursor=-1
        while len(prime_factors)>1:
            if H[cursor] in prime_factors:
                prime_factors.remove(H[cursor])
            cursor-=1
        hpf=prime_factors[0]
        H.append(hpf)
    return H

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