

A008864


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


98



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
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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 k1 is prime.  JuriStepan Gerasimov, Sep 08 2009
a(n) = prime(n)+1, a(n)prime(n1) is very often prime, example:
18=prime(7)+1, 18prime(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 baseb digital sum of b, or b = 2 is the only base for which the baseb 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), 221222.


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



