A105052 Write a(n) as a four-bit number; those bits state whether 10n+1, 10n+3, 10n+7 and 10n+9 are primes.

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

Offset: 0

Author

Robert G. Wilson v, Apr 01 2005

Keywords

• base
• nonn
• easy

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 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

Examples

			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
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000040, A007652, A010051.

Cf. A030430, A030431, A030432, A030433.

Indices of 0,...,15: A032352, A216298, A216297, A216308, A216296, A216307, A216306 (also 0), A216299, A216295, A216305, A216304, A216300, A216303, A216301, A216302, A007811.

Cf. A140891 (analog in base 14, prime = bit 0, remainder 1 = LSB), A140387 (analog in base 30, prime = bit 0, remainder 1 = LSB).

Programs

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}]
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 *)

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

Extensions

Edited by Don Reble, Nov 08 2005

Further edited by R. J. Mathar, Jun 18 2008

Further edited by N. J. A. Sloane, Aug 29 2008 at the suggestion of R. J. Mathar