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A105052
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Write a(n) as a four-bit number; those bits state whether 10n+1, 10n+3, 10n+7 and 10n+9 are primes.
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1
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6, 15, 5, 10, 14, 5, 10, 13, 5, 2, 15, 4, 2, 11, 1, 10, 6, 5, 8, 15, 0, 8, 7, 5, 8, 10, 5, 10, 12, 4, 2, 14, 0, 10, 3, 5, 2, 5, 5, 2, 9, 1, 8, 13, 5, 2, 14, 1, 2, 9, 5, 0, 12, 0, 10, 2, 5, 10, 2, 5, 10, 7, 0, 8, 14, 5, 8, 6, 4, 8, 9, 1, 2, 5, 4, 10, 9, 4, 2, 2, 1, 8, 15, 1, 0, 7, 4, 2, 14, 0, 2, 9, 1, 2
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Binary encoding of the prime-ness of the 4 integers r+10*n with remainder r=1, 3, 7 or 9. Classify the 4 integers 10n+r with r= 1, 3, 7, or 9, as nonprime or prime and associate bit positions 3=MSB,2,1,0=LSB with the 4 remainders in that order. Raise the bit if 10n+r is prime, erase it if 10n+r is nonprime. The sequence inteprets the 4 bits as a number in base 2. a(n) is the decimal representation, obviously in the range 0<=a(n)<16. - Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Jun 10 2008
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EXAMPLE
| For n=2, the 4 numbers 21 (r=1), 23 (r=3), 27 (r=7), 29 (r=9) are nonprime, prime, nonprime, prime, which is rendered into 0101 = 2^0+2^2=5=a(2).
These two hexadecimal lines represent the primes between 10 and 1010:
F5AE5AD52F 42B1A658F0 8758A5AC42 E0A3525529 18D52E1295
0C0A25A25A 708E586489 1254A94221 8F10742E02 912A42A4A1
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MATHEMATICA
| f[n_] := FromDigits[ PrimeQ[ Drop[ Range[10n + 1, 10n + 9, 2], {3, 3}]] /. {True -> 1, False -> 0}, 2]; Table[ f[n], {n, 2, 93}]
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PROG
| (Pari) f(n)={s=0; if(isprime(10*n+1), s+=8); if(isprime(10*n+3), s+= 4); if(isprime(10*n+7), s+=2); if(isprime(10*n+9), s+=1); return(s)}; for(n=0, 93, print1(f(n), ", ")) - W. Bomfim webonfim(AT)bol.com Jan 18, 2011
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CROSSREFS
| Cf. A000040, A007652.
Cf. A030430, A030431, A030432, A030433.
Sequence in context: A013314 A019306 A115408 * A003566 A205149 A070870
Adjacent sequences: A105049 A105050 A105051 * A105053 A105054 A105055
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KEYWORD
| base,nonn,easy
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AUTHOR
| Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 01 2005
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EXTENSIONS
| Edited by Don Reble (djr(AT)nk.ca), Nov 08 2005
Further edited by R. J. Mathar, Jun 18 2008
Further edited by N. J. A. Sloane (njas(AT)research.att.com), Aug 29 2008 at the suggestion of R. J. Mathar
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