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 A006285 Odd numbers not of form p + 2^x (de Polignac numbers). (Formerly M5390) 26
 1, 127, 149, 251, 331, 337, 373, 509, 599, 701, 757, 809, 877, 905, 907, 959, 977, 997, 1019, 1087, 1199, 1207, 1211, 1243, 1259, 1271, 1477, 1529, 1541, 1549, 1589, 1597, 1619, 1649, 1657, 1719, 1759, 1777, 1783, 1807, 1829, 1859, 1867, 1927, 1969, 1973 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Contains both primes (A065381) and composites (A098237). - Jonathan Vos Post, Jun 19 2008 A109925(a(n)) = 0. - Reinhard Zumkeller, May 27 2015 Crocker shows that this sequence is infinite; in particular, 2^2^n - 5 is in this sequence for each n > 2. - Charles R Greathouse IV, Sep 01 2015 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). Clifford A. Pickover, A Passion for Mathematics, John Wiley & Sons, Inc., NJ, 2005, pp. 62 & 300. D. Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, see #127. LINKS T. D. Noe, Table of n, a(n) for n = 1..10000 Roger Crocker, A theorem concerning prime numbers, Mathematics Magazine 34:6 (1961), pp. 316+344. P. Pollack, Not Always Buried Deep, Selections from Analytic and Combinatorial Number Theory, ex. 5.1.6, p. 193, and p. 216 ff. EXAMPLE 127 is in the sequence since 127 - 2^0 = 126, 127 - 2^1 = 125, 127 - 2^2 = 123, 127 - 2^3 = 119, 127 - 2^4 = 111, 127 - 2^5 = 95, and 127 - 2^6 = 63 are all composite. - Michael B. Porter, Aug 29 2016 MAPLE N:= 10000: # to get all terms <= N P:= select(isprime, {2, seq(i, i=3..N, 2)}): T:= {seq(2^i, i=0..ilog2(N))}: R:= {seq(i, i=1..N, 2)} minus {seq(seq(p+t, p=P), t=T)}: sort(convert(R, list)); # Robert Israel, Sep 23 2016 MATHEMATICA Do[ i = 0; l = Ceiling[ N[ Log[ 2, n ] ] ]; While[ ! PrimeQ[ n - 2^i ] && i < l, i++ ]; If[ i == l, Print[ n ] ], {n, 1, 2000, 2} ] Join[{1}, Select[Range[5, 1999, 2], !MemberQ[PrimeQ[#-2^Range[Floor[ Log[ 2, #]]]], True]&]] (* Harvey P. Dale, Jul 22 2011 *) PROG (PARI) isA006285(n, i=1)={ bittest(n, 0) && until( isprime(n-i) || nn } \\ - M. F. Hasler, Jun 19 2008, updated Apr 12 2017 (Haskell) a006285 n = a006285_list !! (n-1) a006285_list = filter ((== 0) . a109925) [1, 3 ..] -- Reinhard Zumkeller, May 27 2015 (MAGMA) lst:=[]; for n in [1..1973 by 2] do x:=-1; repeat x+:=1; a:=n-2^x; until a lt 1 or IsPrime(a); if a lt 1 then Append(~lst, n); end if; end for; lst; // Arkadiusz Wesolowski, Aug 29 2016 CROSSREFS Cf. A133122, A098237, A065381, A156695, A109925, A118954, A232460, A276417. Sequence in context: A126096 A164966 A178088 * A094933 A156702 A180536 Adjacent sequences:  A006282 A006283 A006284 * A006286 A006287 A006288 KEYWORD nonn,nice,easy AUTHOR EXTENSIONS More terms from Larry Reeves (larryr(AT)acm.org), Apr 13 2000 Link to Pollack Notes corrected by Rainer Rosenthal, Feb 03 2009, and M. F. Hasler, Apr 12 2017 STATUS approved

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Last modified May 26 02:35 EDT 2019. Contains 323579 sequences. (Running on oeis4.)