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 1-5 of 5 results.

A039698 Numbers k such that phi(k) + 1 is prime.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 17, 18, 19, 21, 22, 23, 26, 27, 28, 29, 31, 32, 34, 36, 37, 38, 40, 41, 42, 43, 46, 47, 48, 49, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 67, 71, 73, 74, 75, 76, 77, 79, 82, 83, 86, 88, 89, 91, 93, 94, 95, 97, 98, 99, 100, 101, 103
Offset: 1

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Author

Olivier Gérard

Keywords

Comments

Positive integers k for which values of A039649(k) are primes. - Vladimir Shevelev, May 10 2008
For every prime p, the numbers p and 2p are terms of this sequence. - Vladimir Shevelev, May 10 2008
Union of A000040 and A066071. - Ray Chandler, May 26 2008

Examples

			phi(10)+1 = 4+1 = 5, a prime number, so 10 is a term.

Links

Crossrefs

Cf. A000010, A000040, A006093, A039649, A066071, A007614.
Cf. A039689 (complement), A296079 (characteristic function).
Cf. also A065512, A078892, A263028, A248792.

Programs

  • Magma
    [n: n in [1..200] | IsPrime(EulerPhi(n)+1)]; // Vincenzo Librandi, Aug 13 2013
  • Mathematica
    Select[Range[300], PrimeQ[EulerPhi[#] + 1]&] (* Vincenzo Librandi, Aug 13 2013 *)

Extensions

Edited by N. J. A. Sloane, May 21 2008 at the suggestion of R. J. Mathar

A296077 a(n) = 1 if 1 + A002322(n) is prime, 0 otherwise, where A002322 is Carmichael lambda.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1
Offset: 1

Views

Author

Antti Karttunen, Dec 05 2017

Keywords

Comments

Out of the first 65537 values, 39743 are 1's (indicating primes), and 25794 are 0's, indicating nonprimes.

Links

Crossrefs

Characteristic function for A263028.
Cf. A002322, A010051, A263027, A263029 (positions of zeros), A296076, A296079.

Programs

  • Mathematica
    Table[If[PrimeQ[CarmichaelLambda[n]+1],1,0],{n,120}] (* Harvey P. Dale, Sep 23 2020 *)
  • PARI
    A296077(n) = isprime(1+lcm(znstar(n)[2]));

Formula

a(n) = A010051(A263027(n)) = A010051(1+A002322(n)).

A263027 a(n) = A002322(n) + 1, where A002322 is Carmichael lambda.

Original entry on oeis.org

2, 2, 3, 3, 5, 3, 7, 3, 7, 5, 11, 3, 13, 7, 5, 5, 17, 7, 19, 5, 7, 11, 23, 3, 21, 13, 19, 7, 29, 5, 31, 9, 11, 17, 13, 7, 37, 19, 13, 5, 41, 7, 43, 11, 13, 23, 47, 5, 43, 21, 17, 13, 53, 19, 21, 7, 19, 29, 59, 5, 61, 31, 7, 17, 13, 11, 67, 17, 23, 13, 71, 7
Offset: 1

Views

Author

Vincenzo Librandi, Oct 08 2015

Keywords

Comments

The function t(k,n) = A002322(n)+k provides many prime values for k=1: for n up to 1000, for example, it returns 798 primes (with repetitions). On the other hand, for n <= 1000 and odd k from 3 to 11, t(k,n) gives 247, 387, 538, 231, 504 prime values, respectively.
Another function of this type is |A002322(n)-119|, which provides 693 prime values for n <= 1000. [Bruno Berselli, Oct 14 2015]

Links

Crossrefs

Cf. A002322.
Cf. A263028: indices n for which a(n) is prime.
Cf. A263029: indices n for which a(n) is composite.
Cf. also A039649, A296076, A296077.

Programs

  • Magma
    [2] cat [CarmichaelLambda(n)+1: n in [2..100]];
  • Mathematica
    Table[CarmichaelLambda[n] + 1, {n, 1, 100}]
  • PARI
    vector(100, n, 1 + lcm(znstar(n)[2])) \\ Altug Alkan, Oct 08 2015

Extensions

Edited by Bruno Berselli, Oct 14 2015

A263029 Numbers n such that A002322(n) + 1 is not a prime, where A002322 is Carmichael lambda.

Original entry on oeis.org

25, 32, 50, 55, 75, 81, 96, 100, 110, 115, 119, 121, 128, 150, 153, 160, 162, 165, 176, 187, 200, 203, 209, 215, 220, 221, 224, 230, 235, 238, 242, 245, 253, 256, 261, 275, 287, 288, 289, 295, 297, 299, 300, 306, 319, 323, 324, 330, 335, 343, 345, 355
Offset: 1

Views

Author

Vincenzo Librandi, Oct 12 2015

Keywords

Comments

Complement of A263028.

Links

Crossrefs

Cf. A002322, A263027, A263028.
Positions of zeros in A296077.
Cf. also A039689.

Programs

  • Magma
    [n: n in [2..400] | not IsPrime(CarmichaelLambda(n)+1)];
  • Mathematica
    Select[Range[1, 400], ! PrimeQ[CarmichaelLambda[#] + 1] &]
  • PARI
    for(n=1, 1e3, if(isprime((1 + lcm(znstar(n)[2]))) == 0, print1(n", "))) \\ Altug Alkan, Oct 12 2015

A296076 Least number with the same prime signature as 1 + A002322(n), where A002322 is Carmichael's lambda.

Original entry on oeis.org

2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 2, 2, 2, 2, 6, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 2, 2, 2, 2, 2, 6, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 6, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 2, 2, 2, 2, 12, 2, 2, 2, 4, 2
Offset: 1

Views

Author

Antti Karttunen, Dec 05 2017

Keywords

Links

Crossrefs

Cf. A002322, A046523, A263027, A263028 (positions of 2's), A296077, A296078.

Programs

Formula

a(n) = A046523(A263027(n)) = A046523(1+A002322(n)).
Showing 1-5 of 5 results.

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

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