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A036952
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Numbers whose binary expansion is a decimal prime.
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16
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| A100051(f(a(n))) = 1 with f(x) = if x<2 then x else 10*f(floor(x/2)) + x mod 2. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 31 2010]
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EXAMPLE
| 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
| (Maple code from R. J. Mathar, Mar 12 2010)
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) ;
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MATHEMATICA
| f[n_, k_]:=FromDigits[IntegerDigits[n, k]]; lst={}; Do[If[PrimeQ[f[n, 2]], AppendTo[lst, n]], {n, 7!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Mar 12 2010]
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CROSSREFS
| Cf. A020449, A036953-A036964. Union of A156059 and A065720.
Sequence in context: A163153 A091157 A199336 * A065720 A148554 A120937
Adjacent sequences: A036949 A036950 A036951 * A036953 A036954 A036955
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KEYWORD
| nonn,base
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AUTHOR
| Patrick De Geest (pdg(AT)worldofnumbers.com), Jan 04 1999.
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EXTENSIONS
| Entry revised by R. J. Mathar and N. J. A. Sloane, Mar 12 2010.
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