cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A229205 Lucky numbers generated from squarefree numbers.

Original entry on oeis.org

1, 3, 10, 13, 19, 22, 30, 33, 38, 47, 53, 59, 69, 71, 78, 82, 87, 97, 107, 110, 115, 129, 138, 146, 151, 158, 161, 167, 173, 182, 187, 197, 210, 218, 223, 227, 233, 249, 255, 265, 267, 278, 285, 295, 299, 305, 314, 318, 327, 334, 346, 357, 367
Offset: 1

Views

Author

Irina Gerasimova, Sep 16 2013

Keywords

Comments

Follow same procedure that is used to produce the lucky numbers A000959 but start with squarefree numbers A005117 instead of natural numbers.

Examples

			Start with squarefree numbers A005117 = (1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 26, 29, 30,...).
Delete every second number to get (1,_ 3,_ 6,_ 10,_ 13,_ 15,_ 19,_ 22,_ 26,_ 30, ...).
Since the next larger remaining number is 3, delete every 3rd number, to get (1, 3,_ 10, 13,_ 19, 22,_ 30, ...).
The next larger remaining number is 10, so delete every 10th term, etc. Note that "30" will remain in this sequence, but is not among the squarefree numbers indexed by lucky numbers, A229483. - _M. F. Hasler_, Sep 24 2013
		

Crossrefs

Programs

  • PARI
    list_A229205(Nmax)={my(v=(select(issquarefree,vector(Nmax,i,i))),i,k);while(v[i=k+++(v[k]==1)]<=#v,v=vecextract(v,2^#v-1-sum(j=1,#v\v[i],2^(v[i]*j-1))));v} \\ M. F. Hasler, Sep 24 2013

A229483 Squarefree numbers whose indices are lucky numbers.

Original entry on oeis.org

1, 3, 10, 13, 19, 22, 33, 38, 47, 53, 59, 69, 78, 82, 102, 107, 110, 115, 119, 129, 141, 151, 161, 173, 182, 187, 206, 210, 215, 218, 227, 246, 258, 265, 274, 278, 309, 314, 318, 327, 334, 346, 359, 367, 382, 389, 391, 397, 426, 429, 437, 446, 462, 465, 470
Offset: 1

Views

Author

Keywords

Comments

Originally arose as "Lucky numbers generated from squarefree numbers" under the hypothesis that Ulam's sieve (the one used to produce lucky numbers) ignores the values of the terms.

Crossrefs

Formula

a(n) = A005117(A000959(n)). - Charles R Greathouse IV, Sep 16 2013

A229494 Lucky numbers generated from noncomposite numbers.

Original entry on oeis.org

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

Views

Author

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

Keywords

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

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}
Showing 1-3 of 3 results.