A115316 Lexicographically earliest permutation of the natural numbers such that each prime number is followed by exactly two composite numbers.

1, 2, 4, 6, 3, 8, 9, 5, 10, 12, 7, 14, 15, 11, 16, 18, 13, 20, 21, 17, 22, 24, 19, 25, 26, 23, 27, 28, 29, 30, 32, 31, 33, 34, 37, 35, 36, 41, 38, 39, 43, 40, 42, 47, 44, 45, 53, 46, 48, 59, 49, 50, 61, 51, 52, 67, 54, 55, 71, 56, 57, 73, 58, 60, 79, 62, 63, 83, 64, 65, 89, 66

Offset

1,2

Comments

Inverse: A115318.

Fixed points = {1,2,27,28,29,30,33,34}, also for A115317, A115318, A115319.

Links

Table of n, a(n) for n=1..72.

Index entries for sequences that are permutations of the natural numbers

Formula

a(a(n)) = A115317(n).

a(3*n-2) = A018252(2*n-1), a(3*n-1) = A000040(n), a(3*n) = A018252(2*n);

a(n+1+floor((n+1)/2)) = A002808(n).

Mathematica

terms = 72;
np = Ceiling[terms/3] + 1;
nc = Ceiling[(2/3) terms];
pp = Prime[Range[np]];
cc = Partition[Select[Range[FindRoot[n == nc + PrimePi[n] + 1, {n, nc, 2nc}][[1, 2]] // Floor], CompositeQ], 2];
Join[{1}, Riffle[pp, cc] // Flatten][[1 ;; terms]] (* Jean-François Alcover, Nov 15 2021 *)

Crossrefs

Cf. A002808, A018252, A073846.

Cf. A115317, A115318, A115319.

Sequence in context: A236675 A210771 A359535 * A089088 A251622 A073899

Adjacent sequences: A115313 A115314 A115315 * A115317 A115318 A115319

Keyword

nonn,easy

Author

Reinhard Zumkeller, Jan 20 2006

Status

approved