login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A325355 One plus the number of steps applying A325351 (Heinz number of augmented differences of reversed prime indices) to reach a fixed point. 7
1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 1, 2, 1, 1, 4, 1, 1, 1, 2, 1, 2, 1, 1, 3, 1, 1, 5, 1, 4, 2, 1, 1, 6, 1, 1, 4, 1, 1, 3, 1, 1, 1, 2, 2, 7, 1, 1, 2, 3, 1, 8, 1, 1, 3, 1, 1, 4, 1, 5, 5, 1, 1, 9, 4, 1, 2, 1, 1, 3, 1, 5, 6, 1, 1, 2, 1, 1, 4, 4, 1, 10, 1, 1, 3, 5, 1, 11, 1, 6, 1, 1, 2, 5, 2, 1, 7, 1, 1, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,9

COMMENTS

The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).

The augmented differences aug(y) of an integer partition y of length k are given by aug(y)_i = y_i - y_{i + 1} + 1 if i < k and aug(y)_k = y_k. For example, aug(6,5,5,3,3,3) = (2,1,3,1,1,3).

The fixed points of A325351 are the Heinz numbers of hooks A093641.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to Heinz numbers

EXAMPLE

Repeatedly applying A325351 starting with 78 gives 78 -> 66 -> 42 -> 30 -> 18 -> 12, and 12 is a fixed point, so a(78) = 6.

MATHEMATICA

primeptn[n_]:=If[n==1, {}, Reverse[Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]];

aug[y_]:=Table[If[i<Length[y], y[[i]]-y[[i+1]]+1, y[[i]]], {i, Length[y]}];

Table[Length[FixedPointList[Times@@Prime/@aug[primeptn[#]]&, n]]-1, {n, 50}]

PROG

(PARI)

augdiffs(n) = { my(diffs=List([]), f=factor(n), prevpi, pi=0, i=#f~); while(i, prevpi=pi; pi = primepi(f[i, 1]); if(prevpi, listput(diffs, 1+(prevpi-pi))); if(f[i, 2]>1, f[i, 2]--, i--)); if(pi, listput(diffs, pi)); Vec(diffs); };

A325351(n) = factorback(apply(prime, augdiffs(n)));

A325355(n) = { my(u=A325351(n)); if(u==n, 1, 1+A325355(u)); }; \\ Antti Karttunen, Nov 16 2019

CROSSREFS

Positions of 2's are A325359.

Cf. A056239, A093641, A112798, A130091, A289509, A325351, A325352, A325366, A325389, A325394, A325395, A325396.

Sequence in context: A333769 A259396 A328672 * A219093 A062760 A323163

Adjacent sequences:  A325352 A325353 A325354 * A325356 A325357 A325358

KEYWORD

nonn

AUTHOR

Gus Wiseman, Apr 23 2019

EXTENSIONS

More terms from Antti Karttunen, Nov 16 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 28 22:34 EDT 2021. Contains 347717 sequences. (Running on oeis4.)