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A100724
Prime numbers whose binary representations are split into at most 3 runs.
0
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 47, 59, 61, 67, 71, 79, 97, 103, 113, 127, 131, 191, 193, 199, 223, 227, 239, 241, 251, 257, 263, 271, 383, 449, 463, 479, 487, 499, 503, 509, 769, 911, 967, 991, 1009, 1019, 1021, 1031, 1039, 1087, 1151, 1279, 1543, 1567
OFFSET
1,1
COMMENTS
The n-th prime is a term iff A100714(n) <= 3.
LINKS
Eric Weisstein's World of Mathematics, Run-Length Encoding.
EXAMPLE
a(3)=5 is a term because it is the 3rd prime whose binary representation splits into no more than 3 runs: 5_10 = 101_2.
MAPLE
R:= 2, 3: count:= 2:
for d from 2 while count < 100 do
for a from d-1 to 1 by -1 do
for b from 0 to a-1 do
p:= 2*(2^d - 2^a + 2^b)-1;
if isprime(p) then R:= R, p; count:= count+1 fi
od od;
p:= 2^(d+1)-1;
if isprime(p) then R:= R, p; count:= count+1 fi
od:
R; # Robert Israel, Oct 30 2024
MATHEMATICA
Select[Table[Prime[k], {k, 1, 50000}], Length[Split[IntegerDigits[ #, 2]]] <= 3 &]
CROSSREFS
Includes A000668 and A095078.
Sequence in context: A051750 A268109 A283225 * A257658 A182231 A100110
KEYWORD
base,nonn,changed
AUTHOR
Joseph Biberstine (jrbibers(AT)indiana.edu), Dec 11 2004
STATUS
approved