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.

A072055 a(n) = 2*prime(n)+1.

Original entry on oeis.org

5, 7, 11, 15, 23, 27, 35, 39, 47, 59, 63, 75, 83, 87, 95, 107, 119, 123, 135, 143, 147, 159, 167, 179, 195, 203, 207, 215, 219, 227, 255, 263, 275, 279, 299, 303, 315, 327, 335, 347, 359, 363, 383, 387, 395, 399, 423, 447, 455, 459, 467, 479
Offset: 1

Views

Author

Reinhard Zumkeller, Jun 11 2002

Keywords

Links

Crossrefs

Cf. A000040, A005385, A023589, A023590, A023591, A023592, A023593, A072059, A023595, A072060, A072056, A072057, A072058, A072192, A165286, A278230.
One less than A089241. After the initial term equal to A166496.
Row 4 of A286625, column 4 of A286623.

Programs

Formula

a(n) = A089241(n)-1.

A100394 a(n) is the subscript of the greatest prime factor of (2*prime(n) + 1).

Original entry on oeis.org

3, 4, 5, 3, 9, 2, 4, 6, 15, 17, 4, 3, 23, 10, 8, 28, 7, 13, 3, 6, 4, 16, 39, 41, 6, 10, 9, 14, 21, 49, 7, 56, 5, 11, 9, 26, 4, 29, 19, 69, 72, 5, 76, 14, 22, 8, 15, 35, 6, 7, 91, 92, 9, 96, 27, 11, 5, 42, 12, 103, 4, 107, 13, 24, 8, 31, 7, 3, 34, 51, 26, 128, 4, 23, 9, 17, 13, 16, 21, 6
Offset: 1

Views

Author

Labos Elemer, Dec 16 2004

Keywords

Examples

			For n = 1: q = prime(1) = 2; 2*q + 1 = 5; A006530(5) = 5, pi(5) = 3 = a(1).
For n = 25: q = prime(25) = 97; 2*q + 1 = 195 = 3*5*13, whose greatest prime factor is 13, of which the subscript = pi(13) = 6 = a(25).

Links

Crossrefs

Cf. A000040, A000720, A006530, A023590.

Programs

  • Maple
    f:= n -> numtheory:-pi(max(numtheory:-factorset(2*ithprime(n)+1))):
map(f, [$1..100]); # Robert Israel, Jul 08 2018
  • Mathematica
    a[n_] := PrimePi[FactorInteger[2*Prime[n]+1][[-1, 1]]]; Array[a, 100] (* Amiram Eldar, Mar 13 2025 *)
  • PARI
    a(n) = primepi(vecmax(factor(2*prime(n) + 1)[,1])); \\ Michel Marcus, Jul 09 2018; corrected Jun 14 2022

Formula

a(n) = A000720(A006530(2*A000040(n) + 1)) = A000720(A023590(n)).

A100395 The smallest prime number q such that the greatest prime divisor of 2*q+1 equals the n-th prime.

Original entry on oeis.org

13, 2, 3, 5, 19, 59, 47, 11, 43, 139, 277, 61, 107, 23, 79, 29, 457, 167, 461, 109, 197, 41, 311, 727, 151, 257, 53, 163, 2203, 317, 1637, 479, 347, 223, 1283, 863, 733, 83, 1297, 89, 271, 859, 1061, 1871, 2089, 5591, 557, 113, 1259, 349, 1553, 3253, 1129, 2441
Offset: 2

Views

Author

Labos Elemer, Dec 16 2004

Keywords

Comments

The offset is 2 because prime(1)=2 is never a prime factor of an odd number.

Examples

			n=1: a(1)=13 because it is the least prime number such that the greatest prime divisor of 2*13 + 1 = 27 equals 3;
n=2: a(2)=2 because the largest prime divisor of 2*a(2) + 1 = 5 is 5;
n=6: a(6)=19 since the greatest prime factor of 2*19 + 1 = 39 = 3*13 is 13=prime(6).

Links

Crossrefs

Cf. A006530, A023590, A100394.

Programs

  • Maple
    A100395 := proc(n)
    p := ithprime(n) ;
    for i from 1 do
        q := ithprime(i) ;
        numtheory[factorset](2*q+1) ;
        if max(op(%)) = p then
            return q;
        end if;
    end do:
end proc:
seq(A100395(n),n=2..60) ; # R. J. Mathar, Sep 22 2018
  • Mathematica
    gpf[n_] := FactorInteger[n][[-1, 1]]; n = 54; m = Prime[n + 1]; v = Table[0, {m}]; c = 0; p = 2; While[c < n, g = gpf[2*p + 1]; If[g <= m && v[[g]] == 0, c++; v[[g]] = p]; p = NextPrime[p]]; Select[v, # > 0 &] (* Amiram Eldar, Aug 08 2020 *)

Formula

a(n) = Min{x; x is prime number; A006530(2x+1) = prime(n)}.
Showing 1-3 of 3 results.

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