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Absolute difference between largest prime factors of two successive semiprimes.
3

%I #8 Nov 07 2020 15:57:25

%S 1,0,2,2,2,2,4,6,8,2,6,10,12,6,10,16,10,6,8,10,2,18,10,14,26,30,24,26,

%T 14,16,18,16,28,34,16,14,36,42,6,50,20,2,24,48,20,24,58,16,44,42,48,

%U 26,30,60,70,46,30,28,24,20,80,30,34,72,12,62,84,52,36,64,12,78,36,56,96

%N Absolute difference between largest prime factors of two successive semiprimes.

%C Absolute first difference of A084127.

%e a(1) = 1 because 4 = 2*2 and 6 = 2*3 so 3 - 2 = 1;

%e a(2) = 0 because 6 = 2*3 and 9 = 3*3 so 3 - 3 = 0;

%e a(3) = 2 because 9 = 3*3 snd 10 = 2*5 so 5 - 3 = 2.

%t Select[ FactorInteger[ Range[300]], Total[#[[All, 2]]] == 2 &][[All, -1, 1]] // Differences // Abs (* _Jean-François Alcover_, Dec 03 2013 *)

%t Abs[#[[1]]-#[[2]]]&/@(Partition[FactorInteger[#][[-1,1]]&/@Select[ Range[ 300],PrimeOmega[#]==2&],2,1]) (* _Harvey P. Dale_, Nov 07 2020 *)

%Y Cf. A001358, A006530, A084127.

%K easy,nonn

%O 1,3

%A _Giovanni Teofilatto_, Mar 23 2007

%E Edited and extended by _Ray Chandler_, Mar 25 2007