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.

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A236675 If n is prime, then a(n) is the least composite number not occurring earlier, else a(n) is the least prime not occurring earlier.

Original entry on oeis.org

2, 4, 6, 3, 8, 5, 9, 7, 11, 13, 10, 17, 12, 19, 23, 29, 14, 31, 15, 37, 41, 43, 16, 47, 53, 59, 61, 67, 18, 71, 20, 73, 79, 83, 89, 97, 21, 101, 103, 107, 22, 109, 24, 113, 127, 131, 25, 137, 139, 149, 151, 157, 26, 163, 167, 173, 179, 181, 27, 191, 28, 193
Offset: 1

Views

Author

M. F. Hasler, Jan 29 2014

Keywords

Comments

If "composite" is replaced by "nonprime", one gets A026234, a permutation of the integers.

Crossrefs

Cf. A026234, A002808, A018252, A097457, A236675.

Programs

  • PARI
    A236675=n->if(isprime(n),A002808(primepi(n)),prime(n-primepi(n)))
  • PARI
    c=p=1;vector(99,n,if(isprime(n),while(isprime(c++),);c,p=nextprime(p+1)))

Formula

a(n) = A002808(A000720(n)) if n is prime, a(n) = A000040(n-A000720(n)) else.

A236676 The n-th term is the n-th composite if n is prime, and the n-th prime if n is not prime.

Original entry on oeis.org

2, 6, 8, 7, 10, 13, 14, 19, 23, 29, 20, 37, 22, 43, 47, 53, 27, 61, 30, 71, 73, 79, 35, 89, 97, 101, 103, 107, 44, 113, 46, 131, 137, 139, 149, 151, 54, 163, 167, 173, 58, 181, 62, 193, 197, 199, 66, 223, 227, 229, 233, 239, 75, 251, 257, 263, 269, 271, 82
Offset: 1

Views

Author

M. F. Hasler, Jan 29 2014

Keywords

Comments

See A097457 for the (maybe more natural) variant where "n-th composite"(=A002808(n)) is replaced by "n-th nonprime" (=A018252(n)).
Essentially the same as A088608. - R. J. Mathar, Feb 03 2014

Links

Crossrefs

Cf. A026234, A236675.

Programs

  • Mathematica
    Module[{nn=100,prs,cmps,len},cmps=Select[Range[nn],CompositeQ];len= Length[ cmps];prs=Prime[Range[len]];Table[If[PrimeQ[n],cmps[[n]],prs[[n]]],{n,len}]] (* Harvey P. Dale, Dec 27 2022 *)
  • PARI
    A236676 = n->if(isprime(n),A002808(n),prime(n))

Formula

a(n) = A002808(n) if n is prime, a(n) = A000040(n) else.
Showing 1-2 of 2 results.

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