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 A048744 Numbers k such that 2^k - k is prime. 13
 2, 3, 9, 13, 19, 21, 55, 261, 3415, 4185, 7353, 12213, 44169, 60975, 61011, 108049, 182451, 228271, 481801, 500899, 505431, 1015321, 1061095 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS All terms except for the first are odd. - Joerg Arndt, Jul 19 2016 From Iain Fox, Nov 14 2017: (Start) If k is congruent to 5 mod 6, then 3 divides 2^k - k; therefore a(n) is never congruent to 5 mod 6. For even k, 2^k - k is divisible by 2; thus all terms other than 2 are odd. It follows that for n > 1, a(n) is congruent to {1, 3} mod 6. (End) REFERENCES J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 261, p. 70, Ellipses, Paris 2008. LINKS Table of n, a(n) for n=1..23. Henri Lifchitz, Renaud Lifchitz, PRP Top Records. 2^n-n. EXAMPLE 2^55 - 55 = 36028797018963913 is prime, so 55 is a term. MATHEMATICA Do[ If[ PrimeQ[ 2^n - n ], Print[ n ] ], {n, 0, 7353} ] (* Second program: *) Select[Range[8000], PrimeQ[2^# - #] &] (* Michael De Vlieger, Nov 15 2017 *) PROG (PARI) for(n=1, 10^5, if(ispseudoprime(2^n-n), print1(n, ", "))) \\ Derek Orr, Sep 01 2014 CROSSREFS Cf. A000325, A081296, A052007. Sequence in context: A175206 A032486 A123859 * A101234 A233190 A269154 Adjacent sequences: A048741 A048742 A048743 * A048745 A048746 A048747 KEYWORD nonn,nice,hard,more AUTHOR G. L. Honaker, Jr. EXTENSIONS 261 and 3415 found by Warut Roonguthai 4185 and 7353 are probable primes (the latter was found by Jud McCranie). 12213 found by Robert G. Wilson v, Jan 02 2001 More terms from Henri Lifchitz contributed by Ray Chandler, Mar 02 2007 Edited by T. D. Noe, Oct 30 2008 a(22)-a(23) from Henri Lifchitz contributed by Robert Price, Sep 01 2014 STATUS approved

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Last modified June 4 21:13 EDT 2023. Contains 363130 sequences. (Running on oeis4.)