A059987 Lucky numbers generated from primes.

2, 5, 11, 17, 31, 41, 47, 59, 73, 83, 103, 127, 137, 149, 157, 179, 197, 211, 233, 257, 269, 283, 307, 313, 331, 353, 367, 379, 389, 431, 449, 487, 499, 509, 547, 563, 571, 607, 617, 631, 661, 677, 691, 709, 739, 751, 823, 829, 853, 877, 883, 907, 919, 947

Offset: 1

Author

Jason Earls, Mar 13 2001

Keywords

• easy
• nonn

Comments

Follow same procedure that is used to produce the lucky numbers A000959 except use primes instead of natural numbers.

Start with natural numbers, apply sieve of Eratosthenes, then sieve of Ulam. This is an example of composition of sieve operators. Circa 1955, Polish mathematician Stanislaw Ulam (1909-1984) identified a particular sequence which he designated "lucky numbers," which share many properties with primes (density, equivalent of twin primes, equivalent of Goldbach's conjecture). Other "random primes" which generalize the lucky numbers not only almost always satisfy the prime number theorem but also the Riemann Hypothesis. What can be said about composition of such "random primes"? - Jonathan Vos Post, May 08 2007

There is a slight ambiguity, arising from the first step of Ulam's sieve, which is to delete every second number, while in the remainder of the procedure, one deletes every v(k)-th term from the current vector v, with k=2,3,4... (but not k=1 in the 1st step). The present sequence is obtained by deleting in the first step every 2nd prime (thus using k=1 in the first step). - M. F. Hasler, Sep 23 2013

Crossrefs

Cf. A000040, A000959.

Cf. A032605, A229205.

Programs

PARI

list_A059987(N=200)={my(v=primes(N),i);while(v[i++]<=#v,v=vecextract(v,2^#v-1-sum(j=1,#v\v[i],2^(v[i]*j-1))));v} \\ - M. F. Hasler, Sep 22 2013

Extensions

Entry revised by N. J. A. Sloane, Oct 20 2007, at the suggestion of R. J. Mathar