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A036952
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Numbers whose binary expansion is a decimal prime.
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55
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3, 5, 23, 47, 89, 101, 149, 157, 163, 173, 179, 185, 199, 229, 247, 253, 295, 313, 329, 331, 355, 367, 379, 383, 405, 425, 443, 453, 457, 471, 523, 533, 539, 565, 583, 587, 595, 631, 643, 647, 653, 659, 671, 675, 689, 703, 709, 755, 781, 785, 815, 841, 855
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OFFSET
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1,1
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COMMENTS
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A100051(f(a(n))) = 1 with f(x) = if x<2 then x else 10*f(floor(x/2)) + x mod 2. - Reinhard Zumkeller, Mar 31 2010
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LINKS
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K. D. Bajpai, Table of n, a(n) for n = 1..10000
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EXAMPLE
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1 = 1_2 is not a prime.
2 = 10_2 is not OK because 10 = 2*5 is not a prime.
3 = 11_2 is OK because 11 is a prime.
4 = 100_2 is not OK because 100 = 4*25 is not a prime.
5 = 101_2 is OK because 101 is a prime.
7 = 111_2 is not OK because 111 = 3*37.
11 = 1011_2 is not OK because 1011 = 3*337.
313 = 100111001_2 is OK because 100111001 is prime.
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MAPLE
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A007088 := proc(n)
dgs := convert(n, base, 2) ;
add(op(i, dgs)*10^(i-1), i=1..nops(dgs)) ;
end proc:
isA036952 := proc(n)
isprime( A007088(n)) :
end proc:
A036952 := proc(n)
if n =1 then
3;
else
for a from procname(n-1)+1 do
if isA036952(a) then
return a ;
end if;
end do:
end if;
end proc:
seq(A036952(n), n=1..80) ;
# R. J. Mathar, Mar 12 2010
A036952 := proc() if isprime(convert(n, binary)) then RETURN (n); fi; end: seq(A036952(), n=1..1000); # K. D. Bajpai, Jul 04 2014
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MATHEMATICA
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f[n_, k_]:=FromDigits[IntegerDigits[n, k]]; lst={}; Do[If[PrimeQ[f[n, 2]], AppendTo[lst, n]], {n, 7!}]; lst (* Vladimir Joseph Stephan Orlovsky, Mar 12 2010 *)
NestList[NestWhile[# + 2 &, #, ! PrimeQ[FromDigits[IntegerDigits[#2, 2]]] &, 2] &, 3, 52] (* Jan Mangaldan, Jul 02 2020 *)
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PROG
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(PARI) is(n)=my(v=binary(n)); isprime(sum(i=1, #v, v[i]*10^(#v-i))) \\ Charles R Greathouse IV, Jun 28 2013
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CROSSREFS
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Cf. A020449, A036953-A036964.
Union of A156059 and A065720.
Sequence in context: A199336 A214876 A280273 * A065720 A148554 A120937
Adjacent sequences: A036949 A036950 A036951 * A036953 A036954 A036955
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KEYWORD
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nonn,base
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AUTHOR
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Patrick De Geest, Jan 04 1999
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EXTENSIONS
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Entry revised by R. J. Mathar and N. J. A. Sloane, Mar 12 2010
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STATUS
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approved
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