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A262228 Deficiency sequence: a(0) = 1, a(n) is the smallest prime p > a(n-1) such that the product of a(i), 1 <= i < n, is deficient (belongs to A005100). 2
1, 2, 5, 11, 59, 653, 84761, 2763189059, 377406001499268899, 2638619515495963542360422694651593, 135435890329895562961039215198033899386421965445591860752412324961 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The product of the first n+1 terms is the smallest deficient multiple of the product of the first n terms.

The product of any finite number of distinct terms of this sequence is deficient.

LINKS

Table of n, a(n) for n=0..10.

FORMULA

a(n) = A151800(floor(1/(2*(Product_{i=2..n-1} a(i)/(a(i)+1))-1)), where A151800 is the "next larger prime" function.

lim_{n->inf} A001065(Product_{i=0..n} a(i))/(Product_{i=0..n} a(i)) = 1. [Corrected by M. F. Hasler, Dec 04 2017]

Conjecture: log(a(n)) ~ e^(an+b) where a and b are approximately 0.6 and -1.6 respectively.

EXAMPLE

a(3) = 11 because A001065(2*5*7) = A001065(70) = 74 > 70, and A001065(2*5*11) = A001065(110) = 106 < 110.

PROG

(PARI) lista(nn) = {print1(p=1, ", "); vp = [p]; for (n=2, nn, np = nextprime(1+floor(1/(2*prod(i=2, n-1, vp[i]/(vp[i]+1))-1))); vp = concat(vp, np); print1(np, ", "); ); } \\ Michel Marcus, Oct 16 2015

CROSSREFS

Cf. A001065, A005100, A151800.

Sequence in context: A140547 A131480 * A295000 A213073 A267527 A286453

Adjacent sequences:  A262225 A262226 A262227 * A262229 A262230 A262231

KEYWORD

nonn,changed

AUTHOR

Chayim Lowen, Sep 15 2015

STATUS

approved

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Last modified December 11 05:41 EST 2017. Contains 295868 sequences.