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A008864 a(n) = prime(n) + 1. 100
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

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). - Hieronymus Fischer, Apr 10 2014

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

R. P. Boas & N. J. A. Sloane, Correspondence, 1974

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.

Row 2 of A286625, column 2 of A286623.

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 July 23 05:58 EDT 2017. Contains 289686 sequences.