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%I #21 Sep 22 2024 06:15:25
%S 1,3,7,8,14,41,270,277,1595,5899,6320,6668,117221,180037,295677,
%T 587152,703625,4397877,12151726,29573235
%N Indices of records in A078571.
%C Numbers k such that total number of prime factors (with multiplicity) of the average of k-th twin prime pair is a record.
%C The records are 1, 2, 3, 4, 5, 7, 9, 10, 12, 14, 15, 17, 19, ... and the associated twin primes recorded in A086827. - _R. J. Mathar_, Oct 24 2007
%F a(n) = {k such that A001222(A014574(k)) is a record}.
%e a(1) = 1 because A078571(1) = 2, since the average of twin prime pair (3,5) is 4 = 2^2 is a semiprime with two prime factors (with multiplicity).
%e a(2) = 3 because A078571(3) = smallomega(12) = 3.
%e a(3) = 7 because A078571(7) = smallomega(60) = 4.
%e a(4) = 8 because A078571(8) = smallomega(72) = 5.
%e a(5) = 14 because A078571(14) = smallomega(192) = 7.
%e a(6) = 41 because A078571(41) = smallomega(1152) = smallomega(2^7 * 3^2) = 9.
%o (PARI) lista(nn) = {my(r=0, c=0, p=2); forprime(q=3, nn, if(q-p==2, c++; if(bigomega(p+1)>r, r=bigomega(p+1); print1(c, ", "))); p=q); } \\ _Jinyuan Wang_, Apr 01 2020
%Y Cf. A001221, A001359, A006512, A014574, A078571.
%K nonn,more
%O 1,2
%A _Jonathan Vos Post_, Oct 02 2007
%E More terms from _R. J. Mathar_, Oct 24 2007
%E a(13)-a(20) from _Jinyuan Wang_, Apr 01 2020