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A268209
Numbers n of the form 2^k + 1 such that n - k is a prime q (for k >= 0).
3
2, 3, 5, 17, 65, 65537, 262145, 18014398509481985, 288230376151711745, 1267650600228229401496703205377, 1329227995784915872903807060280344577
OFFSET
1,1
COMMENTS
Subsequence of A000051.
Prime terms are in A268210: 2, 3, 5, 17, 65537, ...
Corresponding values of numbers k are in A100361 (numbers n such that 2^n-n+1 is prime).
Corresponding values of primes q are in A100362 (primes of the form 2^n-n+1).
4 out of 5 known Fermat primes (3, 5, 17, 65537) are terms; corresponding values of primes q: 2, 3, 13, 65521.
LINKS
FORMULA
a(n) = A100362(n) + A100361(n).
EXAMPLE
17 = 2^4 + 1 is a term because 17 - 4 = 13 (prime).
257 = 2^8 + 1 is not a term because 257 - 8 = 249 (composite number).
MATHEMATICA
2^# + 1 &@ Select[Range[0, 600], PrimeQ[2^# - # + 1] &] (* Michael De Vlieger, Jan 29 2016 *)
PROG
(Magma) [2^k + 1: k in [0..60] | IsPrime(2^k - k + 1)]
CROSSREFS
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Jan 28 2016
STATUS
approved