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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 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 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.)