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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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2
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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
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OFFSET
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0,1
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COMMENTS
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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 interprets 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, Jun 10 2008
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LINKS
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EXAMPLE
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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
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f[n_] := FromDigits[ PrimeQ[ Drop[ Range[10n + 1, 10n + 9, 2], {3, 3}]] /. {True -> 1, False -> 0}, 2]; Table[ f[n], {n, 2, 93}]
f[n_] := If[ GCD[n, 10] == 1, If[PrimeQ@ n, 1, 0], -1]; FromDigits[#, 2] & /@ Partition[ DeleteCases[ Array[f, 940], -1], 4] (* Robert G. Wilson v, Jun 22 2012 *)
Table[FromDigits[Boole[PrimeQ[10n+{1, 3, 7, 9}]], 2], {n, 0, 100}] (* Harvey P. Dale, Nov 07 2016 *)
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PROG
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(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), ", ")) \\ Washington Bomfim, Jan 18 2011
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CROSSREFS
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KEYWORD
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base,nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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