A036952 Numbers whose binary expansion is a decimal prime.
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
Offset: 1
Examples
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.
Links
Programs
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Maple
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
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 *) -
PARI
is(n)=my(v=binary(n));isprime(sum(i=1,#v,v[i]*10^(#v-i))) \\ Charles R Greathouse IV, Jun 28 2013
Extensions
Entry revised by R. J. Mathar and N. J. A. Sloane, Mar 12 2010
Comments