A140387 -id:A140387 - cp's OEIS frontend

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

Robert G. Wilson v, Apr 01 2005

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

			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

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

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).

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 *)

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

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

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

Original entry on oeis.org

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

Juri-Stepan Gerasimov, Jul 07 2008

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.

			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).

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

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 *)

Corrected and extended by Ray Chandler, Feb 20 2009

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Extensions