The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A301797 a(n) = (4^prime(n) - 1)/3. 0
 5, 21, 341, 5461, 1398101, 22369621, 5726623061, 91625968981, 23456248059221, 96076792050570581, 1537228672809129301, 6296488643826193618261, 1611901092819505566274901, 25790417485112089060398421, 6602346876188694799461995861, 27043212804868893898596335048021 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Also, numbers with a prime number of bits 1 (cf. A001348), interleaved with bits 0. Or: odd numbers with alternating binary digits and a prime Hamming weight A000120, cf. A052294. - M. F. Hasler, Oct 16 2018 LINKS Table of n, a(n) for n=1..16. Opinions on Puzzling.StackExchange about this sequence FORMULA a(n) = A002450(A000040(n)). - Michel Marcus, Mar 27 2018 EXAMPLE For n = 1, the first prime number is 2, so a(1) = (4^2-1)/3 = (16-1)/3 = 15/3 = 5; for n = 2, prime(2) = 3, so a(2) = (4^3-1)/3 = (64-1)/3 = 63/3 = 21; for n = 5, prime(5) = 11, so a(5) = (4^(11)-1)/3 = (4194304-1)/3 = 4194303/3 = 1398101. MATHEMATICA a[n_]:=(4^Prime[n] - 1)/3; Array[a, 50] (* Stefano Spezia, Oct 16 2018 *) PROG (Java) public static int a(int n){ int p = 1; while(n > 0){ p++; if(!new String(new char[p]).matches("(..+?)\\1+|.?")){ n--; } } return ((int) Math.pow(4, p)-1)/3; } (PARI) a(n) = (4^prime(n) - 1)/3; \\ Michel Marcus, Mar 27 2018 (Magma) [(4^NthPrime(n) - 1)/3: n in [1..20]]; // Vincenzo Librandi, Oct 17 2018 CROSSREFS Cf. A000040, A000120. Subsequence of A006995 and of A002450, which is a subsequence of A000975. Also the intersection of A002450 and A052294. Sequence in context: A241467 A267020 A141798 * A015461 A101694 A006109 Adjacent sequences: A301794 A301795 A301796 * A301798 A301799 A301800 KEYWORD nonn,easy AUTHOR André Dalwigk, Mar 26 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 9 02:18 EST 2023. Contains 367681 sequences. (Running on oeis4.)