A119257 A permutation of the positive integers formed by reversing the order of the composites within each run of composites (1 and primes are left alone).

1, 2, 3, 4, 5, 6, 7, 10, 9, 8, 11, 12, 13, 16, 15, 14, 17, 18, 19, 22, 21, 20, 23, 28, 27, 26, 25, 24, 29, 30, 31, 36, 35, 34, 33, 32, 37, 40, 39, 38, 41, 42, 43, 46, 45, 44, 47, 52, 51, 50, 49, 48, 53, 58, 57, 56, 55, 54, 59, 60, 61, 66, 65, 64, 63, 62, 67, 70, 69, 68, 71, 72

Offset

1,2

Links

Alois P. Heinz, Table of n, a(n) for n = 1..20000

Index entries for sequences that are permutations of the natural numbers

Formula

a(n) = Sum_{k=1..2n} floor(cos^2(Pi*(n-1)!^(k-1)/(k-1)!)) - Sum_{k=1..n} floor(cos^2(Pi*(k-1)!^n/n!)). - Anthony Browne, May 24 2016

Example

The run of composites (24,25,26,27,28) becomes (28,27,26,25,24).

Mathematica

Block[{$MaxExtraPrecision = 1000}, Table[Sum[Floor[Cos[Pi (n - 1)!^(k - 1)/(k - 1)!]^2], {k, 2 n}] - Sum[ Floor[Cos[Pi (k - 1)!^n/n!]^2], {k, n}], {n, 72}]] (* Michael De Vlieger, May 24 2016 *)

Prog

(PARI) {m=73; print1(1, ", "); n=2; while(n<=m, while(isprime(n), print1(n, ", "); n++); k=n; while(!isprime(n), n++); forstep(a=n-1, k, -1, print1(a, ", ")))} \\ Klaus Brockhaus, Aug 16 2006

Crossrefs

Sequence in context: A371249 A354369 A199426 * A266645 A376865 A372368

Adjacent sequences: A119254 A119255 A119256 * A119258 A119259 A119260

Keyword

nonn

Author

Leroy Quet, Jul 23 2006

Extensions

More terms from Klaus Brockhaus, Aug 16 2006

Status

approved