|
%I #19 Jan 19 2019 04:15:43
%S 49,57,35,7,24,49,38,49,57,51,40,55,24,7,33,57,32,54,12,23,7,15,38,54,
%T 27,10,1,38,49,59,9,33,15,24,61,35,30,1,54,7,16,43,25,12,39,56,7,41,
%U 57,49,60,43,13,51,19,38,1,40,6,49,54,54,5,3,17,54,14,46,24,49
%N Take next group of 3 primes, beginning at 7, map final digits to base 4 by 1->0, 3->1, 7->3, 9->2; convert back to decimal.
%C The index corresponds to the n-th triple of primes, thus offset is 2 since we discard the first prime triple (2,3,5).
%D Hans Paul van den Haag used this coding in Scientific American, German Edition, 4/1996 P.23.
%H <a href="/index/Fi#final">Index entries for sequences related to final digits of numbers</a>
%e 7,11,13 -> 7,1,3 -> 3 * 4^2 + 0 * 4^1 + 1 * 4^0 = 49.
%e 17,19,23 -> 7,9,3 -> 3 * 4^2 + 2 * 4^1 + 1 * 4^0 = 57.
%t p3[c_]:=FromDigits[(Mod[c,10])/.{1->0,3->1,7->3,9->2},4]; p3/@ Partition[ Prime[ Range[4,220]],3] (* _Harvey P. Dale_, Dec 15 2014 *)
%o (PARI) cod(d) = if (d==1, 0, if (d==3, 1, if (d==7, 3, if (d==9, 2))));
%o a(n) = cod(prime(3*n-2) % 10)*4^2 + cod(prime(3*n-1) % 10)*4 + cod(prime(3*n) % 10); \\ _Michel Marcus_, Aug 16 2013
%K nonn,base
%O 2,1
%A Armand Turpel (armand_t(AT)geocities.com, armand(AT)vo.lu)
%E Offset changed from 7 to 2 by _Michel Marcus_, Aug 16 2013
|
