

A023503


Greatest prime divisor of prime(n)  1.


16



2, 2, 3, 5, 3, 2, 3, 11, 7, 5, 3, 5, 7, 23, 13, 29, 5, 11, 7, 3, 13, 41, 11, 3, 5, 17, 53, 3, 7, 7, 13, 17, 23, 37, 5, 13, 3, 83, 43, 89, 5, 19, 3, 7, 11, 7, 37, 113, 19, 29, 17, 5, 5, 2, 131, 67, 5, 23, 7, 47, 73, 17, 31, 13, 79, 11, 7, 173, 29, 11, 179, 61, 31, 7, 191
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OFFSET

2,1


COMMENTS

Baker & Harman (1998) show that there are infinitely many n such that a(n) > prime(n)^0.677. This improves on earlier work of Goldfeld, Hooley, Fouvry, Deshouillers, Iwaniec, Motohashi, et al.
Fouvry shows that a(n) > prime(n)^0.6683 for a positive proportion of members of this sequence. See Fouvry and also Baker & Harman (1996) which corrected an error in the former work.
The record values are the Sophie Germain primes A005384.  Daniel Suteu, May 09 2017
Conjecture: every prime is in the sequence. Cf. A035095 (see my comment).  Thomas Ordowski, Aug 06 2017
a(n) is 2 for n in A159611, and is at most 3 for n in A174099. Conjecture: liminf a(n) = 3.  Jeppe Stig Nielsen, Jul 04 2020


LINKS

T. D. Noe, Table of n, a(n) for n = 2..10000
R. C. Baker and G. Harman, The BrunTitchmarsh theorem on average, Analytic Number Theory (Proceedings in honor of Heini Halberstam), Birkhauser, Boston, 1996, pp. 39103.
R. Baker and G. Harman, Shifted primes without large prime factors, Acta Arithmetica 83 (1998), pp. 331361.
Etienne Fouvry, Théorème de BrunTitchmarsh; application au théorème de Fermat, Invent. Math 79 (1985), 383407.
D. M. Goldfeld, On the number of primes p for which p + a has a large prime factor, Mathematika 16 (1969), pp. 2327.
R. R. Hall, Some properties of the sequence {p1}, Acta Arith. 28 (1975/76), 101105.
G. Harman, On the greatest prime factor of p1 with effective constants


FORMULA

a(n) = A006530(A006093(n)).  Michel Marcus, Aug 15 2015


MAPLE

A023503 := proc(n)
A006530(ithprime(n)1) ;
end proc:
seq( A023503(n), n=2..80) ; # R. J. Mathar, Sep 07 2016


MATHEMATICA

Table[FactorInteger[Prime[n]  1][[1, 1]], {n, 2, 100}] (* T. D. Noe, Jun 08 2011 *)


PROG

(PARI) a(n) = vecmax(factor(prime(n)1)[, 1]); \\ Michel Marcus, Aug 15 2015


CROSSREFS

Cf. A006093, A006530.
Sequence in context: A203955 A039638 A090926 * A241195 A039640 A053811
Adjacent sequences: A023500 A023501 A023502 * A023504 A023505 A023506


KEYWORD

nonn


AUTHOR

Clark Kimberling


EXTENSIONS

Comments, references, and links from Charles R Greathouse IV, Mar 04 2011


STATUS

approved



