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

1,2

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

Links

Table of n, a(n) for n=1..49.

Example

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.

Prog

(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}

Crossrefs

Cf. A059987, A229205.

Sequence in context: A023215 A185069 A023239 * A211438 A018621 A236940

Adjacent sequences: A229491 A229492 A229493 * A229495 A229496 A229497

Keyword

nonn

Author

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

Status

approved