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%I #25 Oct 19 2017 03:14:40
%S 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,
%T 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,
%U 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
%N Write a(n) as a four-bit number; those bits state whether 10n+1, 10n+3, 10n+7 and 10n+9 are primes.
%C 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
%H Harvey P. Dale, <a href="/A105052/b105052.txt">Table of n, a(n) for n = 0..1000</a>
%e 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).
%e These two hexadecimal lines represent the primes between 10 and 1010:
%e F5AE5AD52F 42B1A658F0 8758A5AC42 E0A3525529 18D52E1295
%e 0C0A25A25A 708E586489 1254A94221 8F10742E02 912A42A4A1
%t f[n_] := FromDigits[ PrimeQ[ Drop[ Range[10n + 1, 10n + 9, 2], {3, 3}]] /. {True -> 1, False -> 0}, 2]; Table[ f[n], {n, 2, 93}]
%t 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 *)
%t Table[FromDigits[Boole[PrimeQ[10n+{1,3,7,9}]],2],{n,0,100}] (* _Harvey P. Dale_, Nov 07 2016 *)
%o (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
%Y Cf. A000040, A007652, A010051.
%Y Cf. A030430, A030431, A030432, A030433.
%K base,nonn,easy
%O 0,1
%A _Robert G. Wilson v_, Apr 01 2005
%E Edited by _Don Reble_, Nov 08 2005
%E Further edited by _R. J. Mathar_, Jun 18 2008
%E Further edited by _N. J. A. Sloane_, Aug 29 2008 at the suggestion of _R. J. Mathar_
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