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A037271
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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 exists.
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23
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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
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OFFSET
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1,1
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COMMENTS
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a(33) is presently unknown: starting with 49, no prime has been reached after 110 steps. See A037274 for the latest information.
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LINKS
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Table of n, a(n) for n=1..32.
Patrick 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
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EXAMPLE
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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.
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MATHEMATICA
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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 *)
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PROG
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(Haskell)
a037271 = length . takeWhile ((== 0) . a010051'') .
iterate a037276 . a002808
-- Reinhard Zumkeller, Apr 03 2012
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CROSSREFS
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Cf. A037272, A037273, A037274, A056938, A002808, A037276, A027746, A230305.
Sequence in context: A258821 A124916 A007418 * A074955 A352571 A245625
Adjacent sequences: A037268 A037269 A037270 * A037272 A037273 A037274
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KEYWORD
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nonn,nice,base,more,hard
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AUTHOR
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Jeff Burch
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STATUS
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approved
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