# [seqfan] Re: More terms for A195265 and A230305 ?

Wouter Meeussen wouter.meeussen at telenet.be
Sun Oct 27 13:00:02 CET 2013

```for those working with Mathematica, using
A080670[n_]:=ToExpression at StringJoin[ToString/@Flatten[DeleteCases[FactorInteger[n],1,-1]]]

For A195265 , the first 40 terms take only one second using
NestWhileList[A080670,  i = 1; 20, (PrintTemporary[{i++, #}]; ! PrimeQ[#])
&, 1, 40]
with a(41)=43467514876394875501133442699882620583081205227 (?check?)

but reproducing Sean A. Irvine's 70 terms (what's a(70)??) "hangs" on the
factorisation of
a(55) which takes 20 minutes to evaluate to
443*56783*740808708312261515244578953559*1683460560567100553060069863617294893

so far:

{1,20},
{2,225},
{3,3252},
{4,223271},
{5,297699},
{6,399233},
{7,715623},
{8,3263907},
{9,32347303},
{10,160720129},
{11,1153139393},
{12,72171972859},
{13,736728093411},
{14,3245576031137},
{15,11295052366467},
{16,310807934835791},
{17,1789205424940407},
{18,31745337977379983},
{19,1122916740775279751},
{20,7251536377635958081},
{21,151243563319717018007},
{22,1121396149754176552459},
{23,75932351114908908171459},
{24,3655130778271255318091789},
{25,14959341367755562901131977},
{26,34986447122585187633710659},
{27,1831215981937332389236978179},
{28,313224835114543391579198264647},
{29,476664358193926455139982941801},
{30,3894553245992691175152795023891},
{31,132746366910908266441840480446403},
{32,14827188440943221883267109923487963},
{33,31677138752258518643179233081330519},
{34,3399439119019280029138988876664839207},
{35,1031091355507223378710949904168165523463},
{36,132411030792311443628391225232966966285737},
{37,3374773953639640292210918919998158514329541},
{38,18118645159964859891117187397348056124388561},
{39,333132143964638500160914816848585652355475611},
{40,4339779194757514315803243245042123341102411963},
{41,43467514876394875501133442699882620583081205227},
{42,321011894373310762051641163853311891567953317269293},
{43,37210435034772092714046118995294856628184376694869347},
{44,349828786497847697248921942850440203857761430075804817},{45,33182917107436506939494287772998973909148874702313377399},{46,1932412735512607965871685923338963030422770854966852116073},{47,37392872225493034699309237157170878572245780852206787837181},{48,412647766390833734444929769855778777948727276473907467474693},{49,3263523000971344529447965690456090974370023735458141834559537},{50,3101454147825427160314861186911479357122687657988115033571385847},{51,321036281528336051353262347964794823559426086863047234824993347497},{52,32577115153710657671790025996243079338204694711072846485862432072479},{53,1326931966641130586734869697712528335278446189676861190808138263245579},{54,317140882604011846805291436949702158923616724598993248351685221569237529},{55,31371196658916949249408693469184893318110299927780186415248775022785466503}
{56,443567837408087083122615152445789535591683460560567100553060069863617294893},
{57,7619860311238375857894724798334256170952046407785111199930594835524474243089},
{58,74103791429418459265255067601793396028700030399997339658865529281088155359653},
{59,894943503775981561080785155900149377793729371846593417011004197342503928416257},
{60,281443108374284771468144750849343901023566934597725978081621220000148571720656603}

hangs again at factoring a(60) ...

Wouter.
ps. doesn't the word 'base' have two meanings in English?

-----Original Message-----
From: Neil Sloane
Sent: Sunday, October 27, 2013 7:56 AM
To: Sequence Fanatics Discussion list
Subject: [seqfan] More terms for A195265 and A230305 ?

Dear Seqfans, A195265 was created in 2011, but presumably we have better
factoring algorithms now and more computers and
more people and a bigger cloud.

applying the map  x -> A080670(x) until you reach a prime;
A195264(20) will be the prime that is reached (or -1 if
no prime is ever reached).

A230305(n) is the number of steps to reach a prime,
starting with n (or -1 if no prime is ever reached).
The question then is, what is A230305(20)?

Could someone extend A195265 and see what happens? (it could also use a
b-file). It /should/ reach a prime sooner or later!

Neil

--
Dear Friends, I have now retired from AT&T. New coordinates:

Neil J. A. Sloane, President, OEIS Foundation
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.