A229494 Lucky numbers generated from noncomposite numbers.

1, 3, 13, 19, 37, 43, 61, 71, 89, 101, 113, 131, 163, 181, 193, 223, 229, 251, 281, 293, 317, 337, 359, 397, 409, 433, 443, 463, 479, 503, 521, 557, 569, 593, 601, 641, 701, 719, 743, 757, 787, 809, 839, 863, 911, 929, 953, 971, 997

Offset: 1

Author

Irina Gerasimova and M. F. Hasler, Sep 24 2013

Keywords

• nonn

Comments

Result of application of "Ulam's sieve" (used to produce the lucky numbers A000959) to the noncomposite numbers A008578 instead of the naturals A000027.

The "Lucky numbers generated from primes", cf. A059987 = (2, 5, 11, 17, ...), form a disjoint subset, because they are a subset of the odd-indexed primes, while the present sequence is the union of {1} and a subset of the even-indexed primes. - M. F. Hasler, Sep 24 2013

Examples

			Start with noncomposite numbers A008578 = (1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, ...). Delete every 2nd number to get (1, 3, 7, 13, 19, 29, 37, ...). Since the next larger remaining number is 3, delete every 3rd term to get (1, 3, 13, 19, 37, ...). Then delete every 13th term, and so on.
		

Crossrefs

Cf. A059987, A229205.

Programs

PARI

list_A229494(N=200)={my(v=concat(1,primes(N)), i=1); until(v[i++]>#v, v=vecextract(v, 2^#v-1-sum(j=1, #v\v[i+(i<2)], 2^(v[i+(i<2)]*j-1)))); v}