

A227761


a(n) is the maximal difference between successive parts in the minimally runlengthencoded unordered partition of n (A227368(n)).


4



0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 1, 0, 2, 1, 0, 0, 1, 1, 1, 0, 1, 1, 2, 0, 0, 1, 1, 0, 1, 0, 1, 1, 2, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 2, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 2, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 2, 0, 0, 1, 1, 1, 1, 1
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OFFSET

0,8


COMMENTS

After n=3, only composites may obtain value 0. (But not all of them do; see A227762.) The first nine n for which a(n)=2 are 7, 13, 23, 33, 47, 61, 79, 97, 119, of which all are primes except 33 and 119. Conjecture: these values are given by A227786.
Are there any terms larger than 2?


LINKS

Antti Karttunen, Table of n, a(n) for n = 0..132


FORMULA

a(0) = a(1) = 0, and for n>1, a(n) = A043276(A163575(A227368(n)))  1.


PROG

(Scheme)
(define (A227761 n) (if (< n 2) 0 ( (A043276 (A163575 (A227368 n))) 1)))
;; Alternative version which uses auxiliary functions DIFF and binexp_to_ascpart which can be found in the Program section of A129594:
(define (A227761v2 n) (if (< n 2) 0 (apply max (DIFF (binexp_to_ascpart (A227368 n))))))


CROSSREFS

A227762 gives the positions of zeros, in other words, such n that their minimally runlengthencoded partition consists of identical parts.
Cf. also A227368 (for the concept of minimally runlengthencoded unordered partition).
Sequence in context: A079127 A056674 A336107 * A037188 A276847 A271231
Adjacent sequences: A227758 A227759 A227760 * A227762 A227763 A227764


KEYWORD

nonn


AUTHOR

Antti Karttunen, Jul 26 2013


STATUS

approved



