login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A225759 Primes p such that A179382((p+1)/2) = (p-1)/16. 2
1217, 1249, 1553, 4049, 4273, 4481, 4993, 5297, 6449, 6481, 6689, 7121, 8081, 8609, 9137, 9281, 10337, 10369, 10433, 11617, 11633, 12577, 13441, 13633, 14321, 14753, 15569, 16417, 16433, 16673, 17137, 18257, 18433, 18481, 19793, 20113, 20353, 23057, 23857 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Let n be a natural number coprime to 10 and let c be the "cycle length of n" (defined below).

Conjecture 1: If n-1=2^x*c for some x<5, then n is prime. If x > 4, the relative density of primes in such numbers is 1.

Conjecture 2: If the period of the decimal expansion of 1/n is n-1 or a divisor of n-1, and if n-1=2^x*c or n+1=2^x*c for some x, then n is prime.

- Lear Young, with contributions from Peter Košinár, Giovanni Resta, Charles R Greathouse IV, May 22 2013

To define the "cycle length of n" (using n=73 as an example):

Step 1 : 73 +  1 =  74. Get the odd part of  74, which is 37

Step 2 : 73 + 37 = 110. Get the odd part of 110, which is 55

Step 3 : 73 + 55 = 128. Get the odd part of 128, which is  1

Continuing this operation (with 73+1) repeats the same steps as above. There are 3 steps in the cycle, so the cycle length of 73 is c=3. (same to A179382((73+1)/2)=3).

More for the "cycle length of n" see link and cross references.

The numbers in the sequence are the values of n in the above conjecture when c=4 in case (1).

LINKS

Lear Young and Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 117 terms from Young)

Hagen von Eitzen, Details of the "cycle length of n"

EXAMPLE

(1217-1)/16 = 76 = A179382(609).

PROG

(PARI) oddres(n)=n>>valuation(n, 2)

cyc(d)=my(k=1, t=1); while((t=oddres(t+d))>1, k++); k

forstep(n=17, 1e4, [32, 16], if(cyc(n)==n>>4 && isprime(n), print1(n", ")))

\\ Charles R Greathouse IV, May 15 2013

CROSSREFS

Analogs with different values of c: A001122 when c=1, A155072 when c=2, A001134 when c=3. A225890 has composite values.

Cf. A179382, A136042 (both sequences related to the way to get the "cycle length of n").

Sequence in context: A235889 A321062 A059287 * A059669 A032628 A175964

Adjacent sequences:  A225756 A225757 A225758 * A225760 A225761 A225762

KEYWORD

nonn

AUTHOR

Lear Young, May 15 2013

EXTENSIONS

Edited by Charles R Greathouse IV, Nov 11 2014

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 2 23:47 EDT 2020. Contains 333194 sequences. (Running on oeis4.)