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A065722
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Primes which when written in base 4 then reinterpreted in base 10 again give primes.
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1
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2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 37, 43, 47, 53, 61, 71, 73, 79, 83, 97, 103, 107, 109, 113, 131, 149, 151, 157, 163, 167, 181, 191, 193, 197, 227, 233, 241, 251, 277, 293, 307, 311, 313, 317, 349, 359, 373, 389, 401, 419, 421, 433, 443, 449, 463, 467, 503
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| In general rebase notation (Marc LeBrun): p(n) = (4) [p] (10).
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LINKS
| Harry J. Smith, Table of n, a(n) for n=1,...,1000
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FORMULA
| Numbers n such that A049084(n)>0 and A049084(A007090(n))>0. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 15 2007
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EXAMPLE
| The decimal prime 29 in base 4 is 131 which is again a prime in base 10.
E.g. 509{10} = 13331{4} is prime but also 13331{10}.
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MAPLE
| A007090 := proc(n) local b4digs ; b4digs := convert(n, base, 4) ; add( op(i, b4digs)*10^(i-1), i=1..nops(b4digs)) ; end: isA065722 := proc(n) local rebase ; if isprime(n) then rebase := A007090(n) ; RETURN(isprime(rebase)) ; else RETURN(false) ; fi ; end: for n from 1 to 1000 do p := ithprime(n) : if isA065722(p) then printf("%d, ", p) ; fi : od : - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 15 2007
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MATHEMATICA
| Select[ Range[505], PrimeQ[ # ] && PrimeQ[ FromDigits[ IntegerDigits[ #, 4]]] & ]
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PROG
| (PARI) baseE(x, b)= { local(d, e=0, f=1); while (x>0, d=x-b*(x\b); x\=b; e+=d*f; f*=10); return(e) } { n=0; for (m=1, 10^9, p=prime(m); b=baseE(p, 4); if (isprime(b), write("b065722.txt", n++, " ", p); if (n==1000, return)) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Oct 27 2009]
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CROSSREFS
| Cf. A065720-A065727, A065361.
Cf. A004678, A107715, A090707.
Sequence in context: A040177 A040184 A040988 * A028864 A067903 A102348
Adjacent sequences: A065719 A065720 A065721 * A065723 A065724 A065725
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KEYWORD
| nonn,base
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AUTHOR
| Patrick De Geest (pdg(AT)worldofnumbers.com), Nov 15 2001.
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), Jul 02 2008 at the suggestion of R. J. Mathar
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