login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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. 23
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

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-Fran├žois 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 1 16:19 EDT 2022. Contains 357149 sequences. (Running on oeis4.)