

A261314


Rocket Sequence 34: a(0)=34, a(n) = A073846(a(n1)).


4



34, 59, 44, 79, 56, 107, 75, 54, 103, 72, 151, 102, 233, 153, 104, 239, 156, 397, 253, 165, 112, 263, 171, 116, 271, 176, 457, 290, 829, 512, 1619, 974, 3469, 2044, 8123, 4696, 20879, 11861, 6807, 3952, 17159, 9786, 47459
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OFFSET

0,1


COMMENTS

A073846(n) is defined as follows: if n = 2m for some integer m, A073846(n) is the mth prime, if n = 2m1 for some integer m, A073846(n) is the mth nonprime.
Consider the (totally) ordered set {n, A073846(n), A073846(A073846(n))...} and let us append to this the ordered set {...b(b(b(n))),b(b(n)),b(n)} where b(m) = A073898(m) is the inverse of A073846. Let us call the result R#(n). It is clear that if m is a value in R#(n), R#(m) is just R#(n) with a different offset. Therefore, unless there is a need to do otherwise, let us denote each sequence by its lowest value. {a(n)} when extended to all integers (the last few unlisted values are ... 36, 61, 45, 34) is R#(34).
A given sequence c(n) can be one of two kinds. It can either be periodic with c(m) = c(0) for some m, or it can include infinitely many distinct values. R#(n) is finite for all n<34. However, this sequence has been checked up to a(86) = 1091595086717 without reaching 34. Instead it seems to be slowly climbing in value in both the negative and positive directions. Hence, its period is either extremely large or nonexistent (infinite). I conjecture that the latter is the case. Thus I dubbed the sequence "Rocket" because, as opposed to the "Hailstone" sequences, it never seems to "fall".


LINKS

Chayim Lowen, Table of n, a(n) for n = 0..86


FORMULA

a(n+1) = A073846(a(n)) = A018252(ceiling(a(n)/2))*A000035(a(n)) + A000040(ceiling(a(n)/2))*A059841(a(n)).
a(n1) = A073898(a(n)) = 2*A010051(a(n))*A000720(a(n)) + (1A010051(a(n)))*(2*A018252(a(n))1).


EXAMPLE

a(1) = A073846(a(0)) = A073846(34) = 59.


MATHEMATICA

f[n_, lim_] := Block[{p = Prime@ Range@ PrimePi@ lim, c, s, a = {34}}, c = Complement[Range@ lim, p]; s = Riffle[Take[c, Length@ p], p]; Do[AppendTo[a, s[[a[[k]]]]], {k, n}]; a]; f[48, 10000000] (* Michael De Vlieger, Aug 26 2015, after Harvey P. Dale at A073846 *)


CROSSREFS

Cf. A073846.
Sequence in context: A103686 A211715 A108610 * A119454 A259952 A259945
Adjacent sequences: A261311 A261312 A261313 * A261315 A261316 A261317


KEYWORD

nonn


AUTHOR

Chayim Lowen, Aug 14 2015


STATUS

approved



