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 exists.

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

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

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

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 A352571 A245625

Adjacent sequences: A037268 A037269 A037270 * A037272 A037273 A037274

Keyword

nonn,nice,base,more,hard

Author

Jeff Burch

Status

approved