

A065381


Primes not of the form p + 2^k, p prime and k >= 0.


12



2, 127, 149, 251, 331, 337, 373, 509, 599, 701, 757, 809, 877, 907, 977, 997, 1019, 1087, 1259, 1549, 1597, 1619, 1657, 1759, 1777, 1783, 1867, 1973, 2203, 2213, 2293, 2377, 2503, 2579, 2683, 2789, 2843, 2879, 2909, 2999, 3119, 3163, 3181, 3187, 3299
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OFFSET

1,1


COMMENTS

Sequence is infinite. For example, Pollack shows that numbers which are 1260327937 mod 2863311360 are not of the form p + 2^k for any prime p and k >= 0, and there are infinitely many primes in this congruence class by Dirichlet's theorem.  Charles R Greathouse IV, Jul 20 2014


LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000
P. Pollack, Not Always Buried Deep: Selections from Analytic and Combinatorial Number Theory, p. 193, ex. 5.1.6, p. 216ff. [?Broken link]
P. Pollack, Not Always Buried Deep: Selections from Analytic and Combinatorial Number Theory, p. 193, ex. 5.1.6, p. 216ff.
Lei Zhou, Between 2^n and primes.


FORMULA

A078687(A049084(a(n))) = 0; subsequence of A118958.  Reinhard Zumkeller, May 07 2006


EXAMPLE

127 is a prime, 1272^0 through 1272^6 are all nonprimes.


MATHEMATICA

fQ[n_] := Block[{k = Floor[Log[2, n]], p = n}, While[k > 1 && ! PrimeQ[p  2^k], k]; If[k > 0, True, False]]; Drop[Select[Prime[Range[536]], ! fQ[#] &], {2}] (* Robert G. Wilson v, Feb 10 2005; corrected by Arkadiusz Wesolowski, May 05 2012 *)


PROG

(Haskell)
a065381 n = a065381_list !! (n1)
a065381_list = filter f a000040_list where
f p = all ((== 0) . a010051 . (p )) $ takeWhile (<= p) a000079_list
 Reinhard Zumkeller, Nov 24 2011
(PARI) is(p)=my(k=1); while(k<p&&!isprime(pk), k*=2); if(k>p, return(isprime(p))); 0 \\ Charles R Greathouse IV, Jul 20 2014


CROSSREFS

Equals A000040 minus A065380.
Cf. A010051, A006285, A102630, A094076, A156695.
Cf. A098237.
Sequence in context: A266993 A139904 A167414 * A274123 A141928 A062588
Adjacent sequences: A065378 A065379 A065380 * A065382 A065383 A065384


KEYWORD

nonn


AUTHOR

Reinhard Zumkeller, Nov 03 2001


EXTENSIONS

Link and crossreference fixed by Charles R Greathouse IV, Nov 09 2008


STATUS

approved



