A246370 - OEIS

A246370

a(1)=0, a(p_n) = 1 + a(n), a(c_n) = a(n), where p_n = n-th prime = A000040(n), c_n = n-th composite number = A002808(n); Also number of nonleading 0-bits in the binary representation of A135141(n).

0, 1, 2, 0, 3, 1, 1, 2, 0, 3, 4, 1, 2, 1, 2, 0, 2, 3, 3, 4, 1, 2, 1, 1, 2, 0, 2, 3, 4, 3, 5, 4, 1, 2, 1, 1, 2, 2, 0, 2, 3, 3, 2, 4, 3, 5, 3, 4, 1, 2, 1, 1, 1, 2, 2, 0, 2, 3, 3, 3, 4, 2, 4, 3, 5, 3, 4, 4, 1, 2, 5, 1, 2, 1, 1, 2, 2, 0, 3, 2, 3, 3, 2, 3, 4, 2, 4, 3, 2, 5, 3, 4, 4, 1, 2, 5, 3, 1, 2, 1, 1, 1, 3, 2, 2, 0, 4, 3, 5, 2, 3, 3, 4, 2, 3, 4, 2, 4, 3, 2

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..32998

FORMULA

a(1) = 1, and for n >= 1, if A010051(n) = 1 [i.e. when n is prime], a(n) = 1 + a(A000720(n)), otherwise a(n) = a(A065855(n)). [A000720(n) and A065855(n) tell the number of primes, and respectively, composites <= n].

a(n) = A080791(A135141(n)). [a(n) tells also the number of nonleading zeros in binary representation of A135141(n)].

a(n) = A000120(A246377(n))-1. [Respectively, one less than the number of 1-bits in 0/1-swapped version of that sequence].

a(n) = A246348(n) - A246369(n) - 1.

EXAMPLE

Consider n=30. It is the 19th composite number in A002808: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, ...

Thus we consider next n=19, which is the 8th prime in A000040: 2, 3, 5, 7, 11, 13, 17, 19, ...

So we proceed with n=8, which is the 3rd composite number, and then with n=3, which is the 2nd prime, and then with n=2 which is the 1st prime, and we have finished.

All in all, it took us 5 steps (A246348(30) = 6 = 5+1) to reach 1, and on the journey, we encountered three primes, 19, 3 and 2, thus a(30) = 3.

PROG

(Scheme, two versions, the first being a direct recurrence employing memoizing definec-macro from Antti Karttunen's IntSeq-library):

(definec (A246370 n) (cond ((= 1 n) 0) ((= 1 (A010051 n)) (+ 1 (A246370 (A000720 n)))) (else (A246370 (A065855 n)))))

(define (A246370 n) (A080791 (A135141 n)))

CROSSREFS

Cf. A000040, A002808, A000720, A065855, A080791, A135141, A246348, A246369, A246377.

Sequence in context: A124754 A357624 A353923 * A362557 A047983 A070812

Adjacent sequences: A246367 A246368 A246369 * A246371 A246372 A246373

KEYWORD

nonn

AUTHOR

Antti Karttunen, Aug 27 2014

STATUS

approved