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A105052 Write a(n) as a four-bit number; those bits state whether 10n+1, 10n+3, 10n+7 and 10n+9 are primes. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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

LINKS

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

EXAMPLE

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

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 *)

PROG

(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

CROSSREFS

Cf. A000040, A007652, A010051.

Cf. A030430, A030431, A030432, A030433.

Sequence in context: A019306 A115408 A327602 * A003566 A205149 A289722

Adjacent sequences:  A105049 A105050 A105051 * A105053 A105054 A105055

KEYWORD

base,nonn,easy

AUTHOR

Robert G. Wilson v, Apr 01 2005

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

STATUS

approved

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Last modified June 1 18:43 EDT 2020. Contains 334762 sequences. (Running on oeis4.)