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.

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A249902 Numbers n such that 2n-1 and sigma(n) are both primes.

Original entry on oeis.org

2, 4, 9, 16, 64, 289, 1681, 2401, 3481, 4096, 15625, 65536, 85849, 262144, 491401, 531441, 552049, 683929, 703921, 734449, 1352569, 1885129, 3411409, 3892729, 5470921, 7091569, 7778521, 9247681, 10374841, 12652249, 18139081, 19439281, 22287841, 23902321
Offset: 1

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Author

Jaroslav Krizek, Nov 14 2014

Keywords

Comments

Intersection of A006254 and A023194.
Sequence is a supersequence of the even superperfect numbers m_k (A061652 or even terms from A019279) because sigma(m_k) = 2*(m_k)-1 = k-th Mersenne prime A000668(k) for k>=1.
Conjecture: 2 and 9 are the only numbers n such that 2n - 1, 2n + 1 and sigma(n) are all primes.

Examples

			289 is in the sequence because 2*289 - 1 = 577 and sigma(289) = 307 (both primes).
		

Crossrefs

Programs

  • Magma
    [n: n in [2..10000000] | IsPrime(2*n-1) and IsPrime(SumOfDivisors(n))];
    
  • Mathematica
    Select[Range[10^7], PrimeQ[2 # - 1] && PrimeQ[DivisorSigma[1, #]] &] (* Vincenzo Librandi, Nov 15 2014 *)
  • PARI
    for(n=1,10^6,if(isprime(2*n-1)&&isprime(sigma(n)),print1(n,", "))) \\ Derek Orr, Nov 14 2014
    
  • Python
    from sympy import isprime, divisor_sigma
    A249902_list = [2]+[n for n in (d**2 for d in range(1,10**3)) if isprime(2*n-1) and isprime(divisor_sigma(n))] # Chai Wah Wu, Jul 23 2016
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