A048986 Home primes in base 2: primes reached when you start with n and (working in base 2) concatenate its prime factors (A048985); repeat until a prime is reached (or -1 if no prime is ever reached). Answer is written in base 10.
1, 2, 3, 31, 5, 11, 7, 179, 29, 31, 11, 43, 13, 23, 29, 12007, 17, 47, 19, 251, 31, 43, 23, 499, 4091, 4091, 127, 4091, 29, 127, 31, 1564237, 59, 4079, 47, 367, 37, 83, 61, 383, 41, 179, 43, 499, 4091, 4091, 47, 683, 127, 173, 113, 173, 53, 191, 4091
Offset: 1
Examples
4 = 2*2 -> 1010 = 10 = 2*5 ->10101 = 21 = 3*7 -> 11111 = 31 = prime.
Links
- Ely Golden, Table of n, a(n) for n = 1..2294
- Patrick De Geest, Home Primes
- Ely Golden, Mersenne Wiki Home Primes base 2
- Ely Golden, Table of n, a(n) for n = 1..3000 (a-file)
Programs
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Mathematica
f[n_] := Module[{fi}, If[PrimeQ[n], n, fi = FactorInteger[n]; Table[ First[#], {Last[#]}]& /@ fi // Flatten // IntegerDigits[#, 2]& // Flatten // FromDigits[#, 2]&]]; a[1] = 1; a[n_] := TimeConstrained[FixedPoint[f, n], 1] /. $Aborted -> -1; Array[a, 55] (* Jean-François Alcover, Jan 01 2016 *) -
Python
from sympy import factorint, isprime def f(n): if n == 1: return 1 return int("".join(bin(p)[2:]*e for p, e in factorint(n).items()), 2) def a(n): if n == 1: return 1 while not isprime(n): n = f(n) return n print([a(n) for n in range(1, 56)]) # Michael S. Branicky, Oct 07 2022 -
SageMath
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 radix=2 index=2 while(index<=1344): print(str(index)+" "+str(hp(index,radix))) index+=1
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