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A065891
The a(n)-th composite number is 2^n.
1
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.
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
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