

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
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OFFSET

1,2


COMMENTS

Numbers k such that total number of prime factors (with multiplicity) of the average of kth 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


LINKS

Table of n, a(n) for n=1..20.


FORMULA

a(n) = {k such that A001222(A014574(k)) is a record)}.
a(n) = {k such that A001222{(A001359(k+1) + A006512(k+1)}/2) is a record)}.
a(n) = {k such that A001222(2*A040040(k)) is a record)}.
a(n) = {k such that A001222(A054735(k+1)/2) is a record)}.
a(n) = {k such that A001222(A111046(k+1)/4) is a record)}.


EXAMPLE

a(1) = 1 because A078571(1) = 2, since the avergae 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(qp==2, c++; if(bigomega(p+1)>r, r=bigomega(p+1); print1(c, ", "))); p=q); } \\ Jinyuan Wang, Apr 01 2020


CROSSREFS

Cf. A001221, A001359, A006512, A014574, A078571.
Sequence in context: A093722 A309745 A002381 * A051211 A105173 A309197
Adjacent sequences: A131556 A131557 A131558 * A131560 A131561 A131562


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



