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A247068
Primes whose base-2 expansion has no two consecutive 1's.
2
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
OFFSET
1,1
COMMENTS
Also: numbers appearing in both A000040 and A003714. Is it known to be infinite?
LINKS
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
MATHEMATICA
Select[Prime[Range[700]], SequenceCount[IntegerDigits[#, 2], {1, 1}]==0&] (* Harvey P. Dale, May 14 2022 *)
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 list(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
Sequence in context: A125822 A025537 A245784 * A028916 A100272 A107630
KEYWORD
nonn,base
AUTHOR
Jeffrey Shallit, Nov 16 2014
STATUS
approved