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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 such number. 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

LINKS

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

P. De Geest, Home Primes

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

CROSSREFS

Cf. A037271-A037275, A056938.

Cf. A010051, A027746.

Sequence in context: A049218 A212358 A154469 * A285313 A231366 A158924

Adjacent sequences:  A037270 A037271 A037272 * A037274 A037275 A037276

KEYWORD

sign,nice,hard,base

AUTHOR

N. J. A. Sloane, Jeff Burch

EXTENSIONS

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

Edited by Charles R Greathouse IV, Apr 23 2010

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

STATUS

approved

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Last modified February 17 16:26 EST 2018. Contains 299296 sequences. (Running on oeis4.)