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 1-4 of 4 results.

A177852 prime(n)-A177687(n).

Original entry on oeis.org

0, 2, 2, 6, 7, 9, 7, 9, 18, 24, 30, 17, 21, 28, 41, 38, 53, 55, 32, 36, 38, 58, 48, 54, 62, 66, 82, 86, 88, 78, 126, 75, 81, 69, 79, 95, 101, 93, 111, 117, 123, 125, 183, 137, 127, 143, 155, 215, 171, 173, 177, 231, 185, 243, 221, 137, 143, 145, 151, 155, 157, 167, 181, 227
Offset: 1

Views

Author

Juri-Stepan Gerasimov, May 14 2010

Keywords

Formula

a(n)=A000040(n)-A177687(n).

Extensions

Keyword:base,less added, most values from a(49) on corrected by R. J. Mathar, May 18 2010

A177959 n-th prime minus number of 0's in binary representation of n-th prime.

Original entry on oeis.org

1, 3, 4, 7, 10, 12, 14, 17, 22, 28, 31, 34, 38, 41, 46, 51, 58, 60, 63, 68, 69, 77, 80, 86, 93, 98, 101, 105, 107, 110, 127, 126, 132, 135, 145, 148, 154, 159, 164, 170, 176, 178, 190, 188, 193, 196, 208, 222, 224, 226, 230, 238, 238, 250, 250, 258, 264, 267, 272, 276
Offset: 1

Views

Author

Juri-Stepan Gerasimov, May 16 2010

Keywords

Crossrefs

Cf. A014499, A035193, A177687.

Programs

  • Maple
    A023416 := proc(n) a := 0 ; for d in convert(n,base,2) do if d = 0 then a := a+1 ; end if; end do; a ; end proc:
A035103 := proc(n) A023416(ithprime(n)) ; end proc:
A177959 := proc(n) ithprime(n)-A035103(n) ; end proc:
seq(A177959(n),n=1..120) ; # R. J. Mathar, May 30 2010

Formula

a(n) = A000040(n) - A035103(n).

Extensions

Corrected (39 removed, 124 replaced by 224, 126 replaced by 226) by R. J. Mathar, May 30 2010

A177962 Number of distinct transpositions of prime factors of n-th composite number.

Original entry on oeis.org

1, 2, 1, 1, 2, 3, 2, 2, 1, 3, 3, 2, 2, 4, 1, 2, 1, 3, 6, 1, 2, 2, 2, 6, 2, 2, 4, 6, 3, 3, 2, 5, 1, 3, 2, 3, 4, 2, 4, 2, 2, 12, 2, 3, 1, 2, 6, 3, 2, 6, 10, 2, 3, 3, 2, 6, 5, 1, 2, 12, 2, 2, 2, 4, 12, 2, 3, 2, 2, 2, 6, 3, 3, 6, 6, 4, 6, 2, 10, 6, 2, 5, 6, 2, 3, 3, 2, 2, 20, 1, 2, 2, 3, 1, 12, 1, 2, 6, 12, 2, 2
Offset: 1

Views

Author

Juri-Stepan Gerasimov, May 16 2010

Keywords

Examples

			a(1)=1 because 1st composite = 4 and (2*2)=1.
a(2)=2 because 2nd composite = 6 and (2*3 or 3*2) = 2.

Crossrefs

Cf. A002808, A177687.

Programs

  • Maple
    A177962 := proc(n) local c; c := A002808(n) ; a := (numtheory[bigomega](c))! ; for p in ifactors(c)[2] do a := a/ op(2,p)! ; end do: a ; end proc:
seq(A177962(n),n=1..120) ; # R. J. Mathar, May 28 2010

Formula

a(n) = A008480(A002808(n)). - R. J. Mathar, May 28 2010

Extensions

Entries checked by R. J. Mathar, May 28 2010

A175520 Number of distinct transpositions of digits (zeros and units) in n-th semiprime written in base 2.

Original entry on oeis.org

3, 3, 6, 6, 4, 1, 10, 10, 10, 10, 15, 15, 20, 20, 15, 15, 20, 15, 6, 15, 15, 6, 21, 35, 35, 35, 35, 35, 35, 21, 21, 21, 21, 7, 35, 7, 21, 21, 7, 21, 21, 7, 28, 56, 56, 70, 70, 56, 56, 56, 56, 56, 28, 56, 70, 70, 70, 70, 28, 56, 28, 56, 70, 70, 56, 56, 56, 70, 56, 56, 28, 56, 56, 28
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Jun 05 2010

Keywords

Examples

			a(1)=3 because (100,010,001) where semiprime(1)=3=100 (in base 2).

Crossrefs

Cf. A177687.

Formula

a(n)=binomial ( (A000120(s)+A023416(s)), A000120(s) ), where s=semiprime(n).

Extensions

a(56) corrected by R. J. Mathar, Jun 07 2010
Showing 1-4 of 4 results.

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