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 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], ! 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 A343184 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

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Last modified October 6 12:35 EDT 2022. Contains 357264 sequences. (Running on oeis4.)