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 A247068 Primes whose base-2 expansion have no two consecutive 1's. 1
 2, 5, 17, 37, 41, 73, 137, 149, 257, 277, 293, 337, 521, 577, 593, 641, 661, 673, 677, 1033, 1061, 1093, 1097, 1109, 1153, 1193, 1289, 1297, 1301, 1321, 1361, 2053, 2069, 2081, 2089, 2113, 2129, 2213, 2309, 2341, 2377, 2389, 2593, 2633, 2689, 2693, 2729, 4129, 4133, 4177, 4229, 4241, 4261, 4357, 4373, 4421, 4649, 4673, 5153, 5189 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Also: numbers appearing in both A000040 and A003714. Is it known to be infinite? LINKS Alois P. Heinz, Table of n, a(n) for n = 1..10000 Estelle Basor, Brian Conrey, Kent E. Morrison, Knots and ones, arXiv:1703.00990 [math.GT], 2017. See page 1. MAPLE M:= 16: # to get all terms < 2^M B1:= {1}: B2:= {}: for n from 2 to M-1 do    B3:= map(`+`, B1, 2^n);    B1:= B1 union B2;    B2:= B3; od: select(isprime, {2} union B1 union B2); # if using Maple 11 or earlier, uncomment the next line # sort(convert(%, list));   # Robert Israel, Nov 16 2014 PROG (Sage) def a_list(M):  # All terms < 2^M. After Robert Israel.     A = [1]; B = [2]; s = 4     for n in range(M-2):         C = [a + s for a in A]         A.extend(B)         B = C         s <<= 1     A.extend(B)     return filter(is_prime, A) a_list(13) # Peter Luschny, Nov 16 2014 (PARI) my(t=bitand(n++, 2*n)); if(t==0, return(n)); my(o=#binary(t)-1); ((n>>o)+1)<

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Last modified January 22 16:36 EST 2018. Contains 298055 sequences.