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 A037271 Number of steps to reach a prime under "replace n with concatenation of its prime factors" when applied to n-th composite number, or -1 if no such number. 22
 2, 1, 13, 2, 4, 1, 5, 4, 4, 1, 15, 1, 1, 2, 3, 4, 4, 1, 2, 2, 1, 5, 3, 2, 2, 1, 9, 2, 9, 6, 1, 15 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(33) is presently unknown: starting with 49, no prime has been reached after 110 steps. See A037274 for the latest information. LINKS P. De Geest, Home Primes M. Herman and J. Schiffman, Investigating home primes and their families, Math. Teacher, 107 (No. 8, 2014), 606-614. Eric Weisstein's World of Mathematics, Home Prime EXAMPLE Starting with 14 (the seventh composite number) we get 14=2*7, 27=3*3*3, 333=3*3*37, 3337=47*71, 4771=13*367, 13367 is prime; so a(7)=5. MATHEMATICA maxComposite = 49; maxIter = 40; concat[n_] := FromDigits[ Flatten[ IntegerDigits /@ Flatten[ Apply[ Table, {#[[1]], {#[[2]]}} & /@ FactorInteger[n], {1}]]]]; composites = Select[ Range[2, maxComposite], ! PrimeQ[#] &]; a[n_] := ( lst = NestWhileList[ concat, composites[[n]], ! PrimeQ[#] &, 1, maxIter]; If[PrimeQ[ Last[lst]], Length[lst] - 1, - 1]); Table[a[n], {n, 1, Length[composites]}] (* Jean-François Alcover, Jul 10 2012 *) PROG (Haskell) a037271 = length . takeWhile ((== 0) . a010051'') .                              iterate a037276 . a002808 -- Reinhard Zumkeller, Apr 03 2012 CROSSREFS Cf. A037272, A037273, A037274, A056938, A002808, A037276, A027746, A230305. Sequence in context: A258821 A124916 A007418 * A074955 A245625 A292947 Adjacent sequences:  A037268 A037269 A037270 * A037272 A037273 A037274 KEYWORD nonn,nice,base,more,hard AUTHOR STATUS approved

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Last modified January 15 20:47 EST 2019. Contains 319184 sequences. (Running on oeis4.)