

A105052


Write a(n) as a fourbit 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
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OFFSET

0,1


COMMENTS

Binary encoding of the primeness 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.  JuriStepan 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 A349083 A205149
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



