Search: id:A037274
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%I A037274
%S A037274 1,2,3,211,5,23,7,3331113965338635107,311,773,11,223,13,13367,1129,
%T A037274 31636373,17,233,19,3318308475676071413,37,211,23,331319,773,3251,13367,
%U A037274 227,29,547,31,241271,311,31397,1129,71129,37,373,313,3314192745739,41,
               379,43,22815088913,3411949,223,47,6161791591356884791277
%N A037274 Home primes: for n >= 2, a(n) = the prime that is finally reached when 
               you start with n, concatenate its prime factors (A037276) and repeat 
               until a prime is reached (a(n) = -1 if no prime is ever reached).
%C A037274 The initial 1 could have been omitted.
%C A037274 Probabilistic arguments give exactly zero for the chance that the sequence 
               of integers starting at n contains no prime, the expected number 
               of primes being given by a divergent sequence - John Conway (conway(AT)math.princeton.edu)
%D A037274 Jeffrey Heleen, Family Numbers: Mathemagical Black Holes, Recreational 
               and Educational Computing, 5:5, pp. 6, 1990.
%D A037274 Jeffrey Heleen, Family numbers: Constructing Primes by Prime Factor Splicing, 
               J. Recreational Math., Vol. 28 #2, 1996-97, pp. 116-119.
%H A037274 P. De Geest, <a href="http://www.worldofnumbers.com/topic1.htm">Home 
               Primes < 100 and Beyond</a>
%H A037274 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               HomePrime.html">Link to a section of The World of Mathematics.</a>
%e A037274 9 = 3*3 -> 33 = 3*11 -> 311, prime, so a(9) = 311.
%e A037274 The trajectory of 8 is more interesting:
%e A037274 8 ->
%e A037274 2 * 2 * 2 ->
%e A037274 2 * 3 * 37 ->
%e A037274 3 * 19 * 41 ->
%e A037274 3 * 3 * 3 * 7 * 13 * 13 ->
%e A037274 3 * 11123771 ->
%e A037274 7 * 149 * 317 * 941 ->
%e A037274 229 * 31219729 ->
%e A037274 11 * 2084656339 ->
%e A037274 3 * 347 * 911 * 118189 ->
%e A037274 11 * 613 * 496501723 ->
%e A037274 97 * 130517 * 917327 ->
%e A037274 53 * 1832651281459 ->
%e A037274 3 * 3 * 3 * 11 * 139 * 653 * 3863 * 5107
%e A037274 and 3331113965338635107 is prime, so a(8) = 3331113965338635107.
%t A037274 f[n_] := FromDigits@ Flatten[ IntegerDigits@ Table[ #[[1]], { #[[2]] 
               }] & /@ FactorInteger@n, 2]; g[n_] := NestWhile[ f@# &, n, !PrimeQ@# 
               &]; g[1] = 1; Array[g, 41] (* Robert G. Wilson v (rgwv(AT)rgwv.com), 
               Sep 22 2007 *)
%Y A037274 Cf. A006919, A037271-A037275, A037276, A037919-A037941, A048986, A056938.
%Y A037274 Cf. also A120716 and related sequences.
%Y A037274 Sequence in context: A106715 A106817 A160759 this_sequence A037275 A142960 
               A117324
%Y A037274 Adjacent sequences: A037271 A037272 A037273 this_sequence A037275 A037276 
               A037277
%K A037274 nonn,nice,base
%O A037274 1,2
%A A037274 N. J. A. Sloane (njas(AT)research.att.com), Jeff Burch (gburch(AT)erols.com)
%E A037274 Corrected and extended by Karl W. Heuer (kwzh(AT)gnu.org), Sep 30 2003

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