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

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A117588 Numbers k such that 2^k + prime(k)^2 is prime. 0
2, 6, 8, 14, 20, 90, 102, 154, 228, 310, 418, 554, 1070, 1224, 3144, 3996, 4464, 16194, 17096, 36642 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
All terms are even since 2^k + prime(k)^2 == 0 (mod 3) for any odd number k. - Robert G. Wilson v, Apr 03 2006
If k is odd, prime(k) == +- 1 (mod 3) making prime(k)^2 == 1 (mod 3) and 2^k == - 1 (mod 3). - Robert G. Wilson v, Apr 03 2006
No more terms below 30000.
LINKS
EXAMPLE
20 is in the sequence because the 20th prime is 71 and 2^20 + 71^2 = 1053617 is prime.
MAPLE
a:=proc(n) if isprime(2^n+ithprime(n)^2) then n else fi end: seq(a(n), n=1..1300); # Emeric Deutsch, Apr 06 2006
MATHEMATICA
Do[ If[ PrimeQ[2^n + Prime[n]^2], Print[n]], {n, 20000}] (* Robert G. Wilson v, Apr 03 2006 *)
PROG
(PARI) for(i=1, 3000, if(isprime(2^i+prime(i)^2), print1(i, ", ")))
CROSSREFS
Sequence in context: A212014 A270050 A137831 * A174229 A187217 A022112
KEYWORD
nonn,more
AUTHOR
Mohammed Bouayoun (mohammed.bouayoun(AT)sanef.com), Apr 03 2006
EXTENSIONS
a(15)-a(19) from Robert G. Wilson v and Giovanni Resta, Apr 03 2006
a(20) from Michael S. Branicky, Feb 10 2023
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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)