

A008864


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


122



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

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
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).  Hieronymus Fischer, Apr 10 2014
Does not contain any number of the format 1+q+....+q^e, q prime, e>=2, i.e., no terms of A060800, A131991, A131992, A131993 etc. [Proof: that requires 1+p = 1+q+...+q^e, or p = q*(1+...+q^(e1)). This is not solvable because the left hand side is prime, the right hand side composite.]  R. J. Mathar, Mar 15 2018


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


FORMULA

a(n) = A000005(A034785(n)) = A000203(A000040(n)) = Sum of divisors of prime(n).  Labos Elemer, May 24 2001
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: A243653 A203444 * A299763 A214583 A232721 A227956
Adjacent sequences: A008861 A008862 A008863 * A008865 A008866 A008867


KEYWORD

nonn,easy


AUTHOR

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


STATUS

approved



