A065891 The a(n)-th composite number is 2^n.

1, 3, 9, 20, 45, 96, 201, 414, 851, 1738, 3531, 7163, 14483, 29255, 58993, 118820, 239143, 480897, 966550, 1941540, 3898356, 7824444, 15699344, 31490742, 63151054, 126614174, 253804612, 508678161, 1019341795, 2042386082, 4091687074, 8196318785, 16416930072

Offset

2,2

Comments

Index of n-th power of 2 in A002808.

Remainder of division 2^n/c(n) equals zero, where c(n) = A002808(n), the n-th composite number.

Exponential increase with a factor > 2 and approaching two.

Links

Table of n, a(n) for n=2..34.

Example

For n = 4, 2^4 = 16 is the 9th composite number: 4,6,8,9,10,12,14,15,16, so a(4) = 9.

Mathematica

Do[s=Mod[2^n, c[n]]; If[s==0, Print[n]], {n, 2, 1000000}]
Table[2^n-(PrimePi[2^n])-1, {n, 2, 31}]

Prog

(PARI) lista(kmax) = {my(c = 0); forcomposite(k = 1, kmax, c++; if(k >> valuation(k, 2) == 1, print1(c, ", "))); } \\ Amiram Eldar, Jun 04 2024

Crossrefs

Cf. A000079, A000720, A002808, A015910, A073800.

Sequence in context: A176163 A203861 A073801 * A321173 A147328 A364914

Adjacent sequences: A065888 A065889 A065890 * A065892 A065893 A065894

Keyword

nonn

Author

Labos Elemer, Nov 28 2001

Extensions

Edited by Robert G. Wilson v, Jun 18 2002

a(32)-a(34) from Amiram Eldar, Jun 04 2024

Status

approved