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A131559
Indices of records in A078571.
0
1, 3, 7, 8, 14, 41, 270, 277, 1595, 5899, 6320, 6668, 117221, 180037, 295677, 587152, 703625, 4397877, 12151726, 29573235
OFFSET
1,2
COMMENTS
Numbers k such that total number of prime factors (with multiplicity) of the average of k-th twin prime pair is a record.
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
FORMULA
a(n) = {k such that A001222(A014574(k)) is a record}.
EXAMPLE
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).
a(2) = 3 because A078571(3) = smallomega(12) = 3.
a(3) = 7 because A078571(7) = smallomega(60) = 4.
a(4) = 8 because A078571(8) = smallomega(72) = 5.
a(5) = 14 because A078571(14) = smallomega(192) = 7.
a(6) = 41 because A078571(41) = smallomega(1152) = smallomega(2^7 * 3^2) = 9.
PROG
(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
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Jonathan Vos Post, Oct 02 2007
EXTENSIONS
More terms from R. J. Mathar, Oct 24 2007
a(13)-a(20) from Jinyuan Wang, Apr 01 2020
STATUS
approved