This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
9 = 3*3 -> 33 = 3*11 -> 311, prime, so a(9) = 311. The trajectory of 8 is more interesting: 8 -> 2 * 2 * 2 -> 2 * 3 * 37 -> 3 * 19 * 41 -> 3 * 3 * 3 * 7 * 13 * 13 -> 3 * 11123771 -> 7 * 149 * 317 * 941 -> 229 * 31219729 -> 11 * 2084656339 -> 3 * 347 * 911 * 118189 -> 11 * 613 * 496501723 -> 97 * 130517 * 917327 -> 53 * 1832651281459 -> 3 * 3 * 3 * 11 * 139 * 653 * 3863 * 5107 and 3331113965338635107 is prime, so a(8) = 3331113965338635107.
b:= n-> parse(cat(sort(map(i-> i[1]$i[2], ifactors(n)[2]))[])): a:= n-> `if`(isprime(n) or n=1, n, a(b(n))): seq(a(n), n=1..48); # Alois P. Heinz, Jan 09 2021
f[n_] := FromDigits@ Flatten[ IntegerDigits@ Table[ #[[1]], { #[[2]] }] & /@ FactorInteger@n, 2]; g[n_] := NestWhile[ f@# &, n, !PrimeQ@# &]; g[1] = 1; Array[g, 41] (* Robert G. Wilson v, Sep 22 2007 *)
step(n)=my(f=factor(n),s="");for(i=1,#f~,for(j=1,f[i,2],s=Str(s,f[i,1]))); eval(s) a(n)=if(n<4,return(n)); while(!isprime(n), n=step(n)); n \\ Charles R Greathouse IV, May 14 2015
from sympy import factorint, isprime
def f(n): return int("".join(str(p)*e for p, e in factorint(n).items()))
def a(n):
if n == 1: return 1
fn = n
while not isprime(fn): fn = f(fn)
return fn
print([a(n) for n in range(1, 40)]) # Michael S. Branicky, Jul 11 2022
def digitLen(x,n):
r=0
while(x>0):
x//=n
r+=1
return r
def concatPf(x,n):
r=0
f=list(factor(x))
for c in range(len(f)):
for d in range(f[c][1]):
r*=(n**digitLen(f[c][0],n))
r+=f[c][0]
return r
def hp(x,n):
x1=concatPf(x,n)
while(x1!=x):
x=x1
x1=concatPf(x1,n)
return x
#example: prints the home prime of 8 in base 10
print(hp(8,10))
15 = 3*5 -> 11.101 -> 11101 = 29, so a(15) = 29.
-- import Data.List (unfoldr) a048985 = foldr (\d v -> 2 * v + d) 0 . concatMap (unfoldr (\x -> if x == 0 then Nothing else Just $ swap $ divMod x 2)) . reverse . a027746_row -- Reinhard Zumkeller, Jul 16 2012
f[n_] := FromDigits[ Flatten[ IntegerDigits[ Flatten[ Table[ #1, {#2}] & @@@ FactorInteger@n], 2]], 2]; Array[f, 64] (* Robert G. Wilson v, Jun 02 2010 *)
from sympy import factorint
def a(n):
if n == 1: return 1
return int("".join(bin(p)[2:]*e for p, e in factorint(n).items()), 2)
print([a(n) for n in range(1, 65)]) # Michael S. Branicky, Oct 07 2022
g[ n_ ] := (x = n; d = {}; While[ FactorInteger[ x ] != {}, f = FactorInteger[ x, FactorComplete -> True ][ [ 1, 1 ] ]; x = x/f; AppendTo[ d, IntegerDigits[ f ] ] ]; FromDigits[ Flatten[ d ] ]); NestList[ g, 8, 15 ]
NestList[FromDigits[Flatten[IntegerDigits/@(Table[First[#],{Last[#]}]& /@ FactorInteger[#])]]&,8,15] (* Harvey P. Dale, Dec 04 2011 *)
first(N, a=8)=vector(N,i,if(i>1,a=A037276(a),a)) \\ M. F. Hasler, Oct 07 2022
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