This site is supported by donations to The OEIS Foundation.

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 (list; graph; refs; listen; history; text; internal format)
 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, 127-2^0 through 127-2^6 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 !! (n-1) 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(kp, 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 cross-reference fixed by Charles R Greathouse IV, Nov 09 2008 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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 3 10:38 EST 2016. Contains 278699 sequences.