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A008864 a(n) = prime(n) + 1. 151
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

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

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^(e-1)). This is not solvable because the left hand side is prime, the right hand side composite.] - R. J. Mathar, Mar 15 2018

1/a(n) is the asymptotic density of numbers whose prime(n)-adic valuation is odd. - Amiram Eldar, Jan 23 2021

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 and N. J. A. Sloane, Correspondence, 1974

Neil Sloane and Brady Haran, Eureka Sequences, Numberphile video (2021)

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)

a(n) = A054640(n)/A054640(n-1). - Flávio V. Fernandes, Mar 20 2021

MAPLE

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

MATHEMATICA

Prime[Range[70]]+1 (* Vladimir Joseph Stephan Orlovsky, Apr 27 2008 *)

PROG

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

(PARI) A008864(n) = (1+prime(n)); \\ Antti Karttunen, Mar 14 2021

(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

(Sage) [nth_prime(n) +1 for n in (1..70)] # G. C. Greubel, May 20 2019

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.

Column 1 of A341605, column 2 of A286623 and of A328464.

Sequence in context: A250122 A243653 A203444 * A299763 A214583 A232721

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 October 19 20:01 EDT 2021. Contains 348091 sequences. (Running on oeis4.)