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A008864 a(n) = prime(n) + 1. 99
3, 4, 6, 8, 12, 14, 18, 20, 24, 30, 32, 38, 42, 44, 48, 54, 60, 62, 68, 72, 74, 80, 84, 90, 98, 102, 104, 108, 110, 114, 128, 132, 138, 140, 150, 152, 158, 164, 168, 174, 180, 182, 192, 194, 198, 200, 212, 224, 228, 230, 234, 240, 242, 252, 258, 264, 270, 272, 278, 282, 284 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Number of divisors of 2^p = p+1 = A000005(A034785(n)) = A000203(A000040(n)) = Sum of divisors of primes. - Labos Elemer, May 24 2001

Or, three together with nonprime numbers k such that k-1 is prime. - Juri-Stepan Gerasimov, Sep 08 2009

a(n) = prime(n)+1, a(n)-prime(n-1) is very often prime, example:

18=prime(7)+1, 18-prime(6)=5 prime, prime(6)=13 & prime(7)=17, so even numbers a(n) = prime(n)+1 are very often the sum of two different primes for n>3. - Pierre CAMI, Nov 27 2013

For n > 1, there are a(n) more nonnegative Hurwitz quaternions than nonnegative Lipschitz quaternions, which are counted in A239396 and A239394, respectively. - T. D. Noe, Mar 31 2014

From Hieronymus Fischer, Apr 10 2014 (Start):

  These are the numbers which are in A239708 or in A187813, but excluding the first 3 terms of A187813, i.e., a number m is a term if and only if m is a term > 2 of A187813, or m is the sum of two distinct powers of 2 such that m - 1 is prime. This means that a number m is a term if and only if m is a term > 2 such that there is no base b with a base-b digital sum of b, or b = 2 is the only base for which the base-b digital sum of m is b. a(6) is the only term such that a(n) = A187813(n); for n < 6, we have a(n) > A187813(n), and for n > 6, we have a(n) < A187813(n). (End)

REFERENCES

C. W. Trigg, Problem #1210, Series Formation, J. Rec. Math., 15 (1982), 221-222.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = A084920(n) / A006093(n). - Reinhard Zumkeller, Aug 06 2007

a(n) = A000040(n) + 1 = A052147(n) - 1 = A113395(n) - 2 = A175221(n) - 3 = A175222(n) - 4 = A139049(n) - 5 = A175223(n) - 6 = A175224(n) - 7 = A140353(n) - 8 = A175225(n) - 9. - Jaroslav Krizek, Mar 06 2010

A239703(a(n)) <= 1. - Hieronymus Fischer, Apr 10 2014

From Ilya Gutkovskiy, Jul 30 2016: (Start)

a(n) ~ n*log(n).

Product_{n>=1} (1 + 2/(a(n)*(a(n) - 2))) = 5/2. (End)

MAPLE

A008864:=n->ithprime(n)+1; seq(A008864(n), n=1..50); # Wesley Ivan Hurt, Apr 11 2014

MATHEMATICA

Table[Prime[n]+1, {n, 30}] (* Vladimir Joseph Stephan Orlovsky, Apr 27 2008 *)

PROG

(PARI) forprime(p=2, 1e3, print1(p+1", ")) \\ Charles R Greathouse IV, Jun 16 2011

(Haskell)

a008864 = (+ 1) . a000040

-- Reinhard Zumkeller, Sep 04 2012, Oct 08 2012

(MAGMA) [NthPrime(n)+1: n in [1..70]]; // Vincenzo Librandi, Jul 30 2016

CROSSREFS

a(n) = prime(n)+1 = A000040(n) + 1 = A000040(n) + A000012(n).

Cf. A000040, A060800, A131991, A131992, A131993, A141468.

Cf. A007953, A079696, A187813, A239703, A239708.

Sequence in context: A250122 A243653 A203444 * A214583 A232721 A227956

Adjacent sequences:  A008861 A008862 A008863 * A008865 A008866 A008867

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, R. K. Guy

STATUS

approved

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Last modified April 25 08:38 EDT 2017. Contains 285348 sequences.