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A037273 Number of steps to reach a prime under "replace n with concatenation of its prime factors", or -1 if no prime is ever reached. 30
-1, 0, 0, 2, 0, 1, 0, 13, 2, 4, 0, 1, 0, 5, 4, 4, 0, 1, 0, 15, 1, 1, 0, 2, 3, 4, 4, 1, 0, 2, 0, 2, 1, 5, 3, 2, 0, 2, 1, 9, 0, 2, 0, 9, 6, 1, 0, 15 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Starting with 49, no prime has been reached after 79 steps.

a(49) > 118, see A056938 and FactorDB link. - Michael S. Branicky, Nov 19 2020

LINKS

Table of n, a(n) for n=1..48.

Patrick De Geest, Home Primes

FactorDB, Home prime base 10

Eric Weisstein's World of Mathematics, Home Prime

EXAMPLE

13 is already prime, so a(13) = 0.

Starting with 14 we get 14 = 2*7, 27 = 3*3*3, 333 = 3*3*37, 3337 = 47*71, 4771 = 13*367, 13367 is prime; so a(14) = 5.

MATHEMATICA

nxt[n_] := FromDigits[Flatten[IntegerDigits/@Table[#[[1]], {#[[2]]}]&/@ FactorInteger[n]]]; Table[Length[NestWhileList[nxt, n, !PrimeQ[#]&]] - 1, {n, 48}] (* Harvey P. Dale, Jan 03 2013 *)

PROG

(Haskell)

a037273 1 = -1

a037273 n = length $ takeWhile ((== 0) . a010051) $

   iterate (\x -> read $ concatMap show $ a027746_row x :: Integer) n

-- Reinhard Zumkeller, Jan 08 2013

(PARI) row_a027746(n, o=[1])=if(n>1, concat(apply(t->vector(t[2], i, t[1]), Vec(factor(n)~))), o) \\ after M. F. Hasler in A027746

tonum(vec) = my(s=""); for(k=1, #vec, s=concat(s, Str(vec[k]))); eval(s)

a(n) = if(n==1, return(-1)); my(x=n, i=0); while(1, if(ispseudoprime(x), return(i)); x=tonum(row_a027746(x)); i++) \\ Felix Fröhlich, May 17 2021

(Python)

from sympy import factorint

def a(n):

    if n < 2: return -1

    klst, f = [n], sorted(factorint(n, multiple=True))

    while len(f) > 1:

        klst.append(int("".join(map(str, f))))

        f = sorted(factorint(klst[-1], multiple=True))

    return len(klst) - 1

print([a(n) for n in range(1, 49)]) # Michael S. Branicky, Aug 02 2021

CROSSREFS

Cf. A037271, A037272, A037274, A037275, A056938.

Cf. A010051, A027746.

Sequence in context: A344178 A154469 A344584 * A285313 A231366 A158924

Adjacent sequences:  A037270 A037271 A037272 * A037274 A037275 A037276

KEYWORD

sign,nice,hard,base,more

AUTHOR

N. J. A. Sloane, Jeff Burch

EXTENSIONS

Edited by Charles R Greathouse IV, Apr 23 2010

a(1) = -1 by Reinhard Zumkeller, Jan 08 2013

Name edited by Felix Fröhlich, May 17 2021

STATUS

approved

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Last modified September 24 15:33 EDT 2021. Contains 347643 sequences. (Running on oeis4.)