A140891 Binary encoding of the prime-ness of the 6 integers r+14*n with remainder r=1, 3, 5, 9, 11 or 13.

9, 49, 20, 42, 41, 20, 27, 33, 62, 10, 39, 21, 11, 39, 60, 30, 49, 28, 43, 41, 28, 31, 49, 55, 14, 53, 53, 42, 51, 29, 14, 51, 22, 58, 45, 22, 59, 57, 55, 46, 37, 29, 11, 43, 60, 14, 53, 60, 42, 59, 54, 27, 43, 54, 26, 61, 29, 15, 39, 28, 31, 49, 23, 58, 47, 54, 27, 53, 62, 42

Offset: 0

Author

Juri-Stepan Gerasimov, Jul 07 2008

Keywords

• nonn
• base

Comments

Classify all integers 14n+r with r= 1, 3, 5, 9, 11 or 13 as nonprime or prime and assign hit positions 0=LSB, 1, 2, 3, 4, 5=MSB to the 6 remainders in the same order. Raise the bit if 14n+r is nonprime, erase it if 14n+r is prime.

The sequence interprets this as a number in base 2 and shows the decimal representation.

Examples

			For n=2, the 6 numbers 29 (r=1), 31 (r=3), 33 (r=5), 37 (r=9), 39 (r=11) and 41 (r=13) are prime, prime, nonprime, prime, nonprime, prime, which is rendered into the binary 001010 = 2^2+2^4=4+16=20=a(2).
		

Crossrefs

Cf. A105052 (analog in base 10, prime = bit 1, remainder 1 = MSB), A140387 (analog in base 30, prime = bit 0, remainder 1 = LSB).

Programs

Mathematica

f[n_]:=FromDigits[1-Boole[PrimeQ[({13,11,9,5,3,1}+14n)]],2]; Table[f[n],{n,0,100}] (* Ray Chandler, Feb 20 2009 *)

Extensions

Corrected and extended by Ray Chandler, Feb 20 2009