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 1-2 of 2 results.

A348446 a(n) = A307720(2*n-1) - A307220(2*n).

Original entry on oeis.org

0, 1, 2, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 4, 4, 4, 6, 6, 6, 5, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 4, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 1, 1, 1, 1, 1, 1, 1
Offset: 1

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Author

N. J. A. Sloane, Oct 22 2021

Keywords

Comments

My guess is that this changes signs infinitely often, but is more likely to be positive than negative. Perhaps the behavior is akin to that of A066520, which shows the "great prime race" between primes congruent to 3 mod 4 and primes congruent to 1 mod 4.
See also the graphs in A307720 and A348248.

Links

Crossrefs

Cf. A066520, A307720, A307730, A348248.

Programs

  • Python
    from itertools import islice
from collections import Counter
def A348446(): # generator of terms. Greedy algorithm
    a = 1
    c, b = Counter(), 1
    while True:
        k, kb = 1, b
        while c[kb] >= kb:
            k += 1
            kb += b
        c[kb] += 1
        b = k
        a2 = k
        yield a-a2
        k, kb = 1, b
        while c[kb] >= kb:
            k += 1
            kb += b
        c[kb] += 1
        b = k
        a = k
A348446_list = list(islice(A348446(),100)) # Chai Wah Wu, Oct 23 2021

A278611 Bases b > 1 that set a new record for the size of the smallest base-b Wieferich prime.

Original entry on oeis.org

2, 6, 34
Offset: 1

Views

Author

Felix Fröhlich, Nov 23 2016

Keywords

Comments

Numbers n such that A039951(n) reaches a new record value.
a(1) = 2. Thereafter smallest number x that occurs later in column 1 of A244249 than any y with 1 < y < x.
Let b(n) be the sequence of corresponding smallest Wieferich primes. b(1)-b(3) are 1093, 66161 and 46145917691, respectively (cf. A307220).
No term is a perfect power, since then its smallest Wieferich prime is at most the size of the smallest Wieferich prime of the base that is raised to a power.
a(4) is either 47, 72 or 139, depending on which of those bases is the smallest where any Wieferich prime exists. The smallest base-139 Wieferich prime is 1822333408543 and any Wieferich primes in bases 47 and 72 are larger than 1.07*10^14 (cf. Fischer).

Examples

			a(2) = 6, since the smallest base-6 Wieferich prime is 66161 and that prime is the second term with a record value in A039951.

Links

Crossrefs

Cf. A039951, A244249, A307220.

Programs

  • PARI
    smallest_w_prime(n) = forprime(p=1, , if(Mod(n, p^2)^(p-1)==1, return(p)))
my(r=0, b=2); while(1, if(smallest_w_prime(b) > r, print1(b, ", "); r=smallest_w_prime(b)); b++)
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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