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Differences between consecutive primes that are not powers of 2 in order of their appearance. Differences which are powers of 2 are omitted from A001223.
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%I #15 Feb 16 2025 05:39:44

%S 6,6,6,6,6,6,6,14,6,10,6,6,6,6,10,12,12,6,10,6,6,6,6,10,14,14,6,10,6,

%T 6,6,6,10,10,6,6,12,6,12,18,6,10,6,6,6,10,6,6,6,6,12,10,6,6,12,6,10,

%U 10,6,6,6,14,10,12,10,10,14,14,20,10,6,6,14,6,6,6,12,6,10,6,10,10,6,18,6,6,6

%N Differences between consecutive primes that are not powers of 2 in order of their appearance. Differences which are powers of 2 are omitted from A001223.

%H Amiram Eldar, <a href="/A082509/b082509.txt">Table of n, a(n) for n = 1..10000</a>

%t Do[s=Log[2, Prime[n+1]-Prime[n]]; If[ !IntegerQ[s], Print[Prime[n+1]]], {n, 1, 1000}]

%t Module[{nn=250,twos},twos=2^Range[0,Floor[Log[2,Prime[nn]]]];Select[ Differences[ Prime[Range[nn]]],!MemberQ[twos,#]&]] (* _Harvey P. Dale_, Apr 18 2012 *)

%o (PARI) list(lim) = {my(p = 2, d); forprime(q = 3, lim, d = q - p; if(d >> valuation(d, 2) > 1, print1(d, ", ")); p = q);} \\ _Amiram Eldar_, Feb 16 2025

%Y Cf. A001223, A082508.

%K nonn,changed

%O 1,1

%A _Labos Elemer_, Apr 28 2003