OFFSET
1,1
COMMENTS
Primes prime(k) such that A049076(k)=1, sorted along increasing k. - R. J. Mathar, Jan 28 2014
REFERENCES
C. Kimberling, Fractal sequences and interspersions, Ars Combinatoria, vol. 45 p 157 1997.
LINKS
R. Zumkeller, Table of n, a(n) for n = 1..1000
Lubomir Alexandrov, On the nonasymptotic prime number distribution, arXiv:math/9811096 [math.NT], 1998.
N. Fernandez, An order of primeness, F(p)
N. Fernandez, An order of primeness [cached copy, included with permission of the author]
FORMULA
A175247 U { a(n); n > 1 } = A000040. { a(n) } = { 2 } U { primes (A000040) with composite index (A002808) }. - Jaroslav Krizek, Mar 13 2010
G.f. over nonprime powers: Sum_{k >= 1} prime(k)*x^k-prime(prime(k))*x^prime(k). - Benedict W. J. Irwin, Jun 11 2016
MAPLE
MATHEMATICA
Prime[ Select[ Range[75], !PrimeQ[ # ] &]] (* Robert G. Wilson v, Mar 15 2004 *)
With[{nn=100}, Pick[Prime[Range[nn]], Table[If[PrimeQ[n], 0, 1], {n, nn}], 1]] (* Harvey P. Dale, Aug 14 2020 *)
PROG
(Haskell)
a007821 = a000040 . a018252
a007821_list = map a000040 a018252_list
-- Reinhard Zumkeller, Jan 12 2013
(PARI) forprime(p=2, 1e3, if(!isprime(primepi(p)), print1(p, ", "))) \\ Felix Fröhlich, Aug 16 2014
(Python)
from sympy import primepi
def A007821(n):
def bisection(f, kmin=0, kmax=1):
while f(kmax) > kmax: kmax <<= 1
while kmax-kmin > 1:
kmid = kmax+kmin>>1
if f(kmid) <= kmid:
kmax = kmid
else:
kmin = kmid
return kmax
def f(x): return n+x-(p:=primepi(x))+primepi(p)
return bisection(f, n, n) # Chai Wah Wu, Oct 19 2024
CROSSREFS
Cf. A049076, A049078, A049079, A049080, A049081, A058322, A058324, A058325, A058326, A058327, A058328, A093046, A006450.
KEYWORD
nonn
AUTHOR
Monte J. Zerger (mzerger(AT)cc4.adams.edu), Clark Kimberling
EXTENSIONS
Edited by M. F. Hasler, Jul 31 2015
STATUS
approved