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.

A377176 Primes p such that 7/2 is a primitive root modulo p.

Original entry on oeis.org

3, 17, 19, 23, 29, 37, 41, 59, 73, 79, 83, 89, 109, 127, 139, 149, 191, 197, 227, 239, 251, 257, 263, 277, 283, 307, 313, 317, 353, 359, 373, 389, 409, 419, 431, 433, 467, 487, 521, 523, 541, 557, 563, 577, 587, 593, 599, 601, 619, 643, 653, 691, 701, 761, 769, 821, 857, 863, 919, 929, 937, 967, 991
Offset: 1

Views

Author

Jianing Song, Oct 18 2024

Keywords

Comments

If p is a term in this sequence, then 7/2 is not a square modulo p (i.e., p is in A038886).
Conjecture: this sequence has relative density equal to Artin's constant (A005596) with respect to the set of primes.

Links

Crossrefs

Primes p such that +a/2 is a primitive root modulo p: A320384 (a=3), A377174 (a=5), this sequence (a=7), A377178 (a=9).
Primes p such that -a/2 is a primitive root modulo p: A377172 (a=3), A377175 (a=5), A377177 (a=7), A377179 (a=9).
Cf. A038886, A005596.

Programs

  • PARI
    print1(3, ", "); forprime(p=11, 10^3, if(znorder(Mod(-5/2, p))==p-1, print1(p, ", ")));

A035196 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m = 14.

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A038885, A038886.

Programs

  • Mathematica
    a[n_] := If[n < 0, 0, DivisorSum[n, KroneckerSymbol[14, #] &]]; Table[ a[n], {n, 1, 100}] (* G. C. Greubel, Apr 27 2018 *)
  • PARI
    my(m=14); direuler(p=2,101,1/(1-(kronecker(m,p)*(X-X^2))-X))
  • PARI
    a(n) = sumdiv(n, d, kronecker(14, d)); \\ Amiram Eldar, Nov 18 2023

Formula

From Amiram Eldar, Nov 18 2023: (Start)
a(n) = Sum_{d|n} Kronecker(14, d).
Multiplicative with a(p^e) = 1 if Kronecker(14, p) = 0 (p = 2 or 7), a(p^e) = (1+(-1)^e)/2 if Kronecker(14, p) = -1 (p is in A038886), and a(p^e) = e+1 if Kronecker(14, p) = 1 (p is in A038885 \ {2, 7}).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2*log(4*sqrt(14)+15)/(2*sqrt(14)) = 0.908710783123... . (End)
Showing 1-2 of 2 results.

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

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