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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)<<o

n=0; while(n<1e6, if(isprime(n=step(n)), print1(n", "))) \\ Charles R Greathouse IV, Nov 16 2014

CROSSREFS

Cf. A000040, A003714.

Sequence in context: A125822 A025537 A245784 * A028916 A100272 A107630

Adjacent sequences:  A247065 A247066 A247067 * A247069 A247070 A247071

KEYWORD

nonn,base

AUTHOR

Jeffrey Shallit, Nov 16 2014

STATUS

approved

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