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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. 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(1) = 1 by convention.

The first binary home prime that is not known is a(2295) - Ely Golden, Jan 09 2017

LINKS

Ely Golden, Table of n, a(n) for n = 1..2294

P. 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)

EXAMPLE

4 = 2*2 -> 1010 = 10 = 2*5 ->10101 = 21 = 3*7 -> 11111 = 31 = prime.

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-Fran├žois Alcover, Jan 01 2016 *)

PROG

(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 xrange(len(f)):

        for d in xrange(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

CROSSREFS

Cf. A048985, A037274, A049065.

Sequence in context: A217370 A088115 A230627 * A093712 A035514 A114009

Adjacent sequences:  A048983 A048984 A048985 * A048987 A048988 A048989

KEYWORD

nonn,base,nice,changed

AUTHOR

Michael B Greenwald (mbgreen(AT)central.cis.upenn.edu)

STATUS

approved

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Last modified January 24 08:40 EST 2017. Contains 281234 sequences.