%I #37 Jun 26 2015 10:10:19
%S 9,16,26,42
%N Doubly prime home primes (DPHP).
%C Take all the factors generated during the search for a home prime, put them together in the order found (just like when looking for the home prime itself) and test for primality. If it is a prime you have a DPHP.
%C Further terms are 74, 75, 95.
%C The number of iterations must be more than 1, preventing numbers such as 12 (12->2*2*3->223) from being a DPHP. - _Dana Jacobsen_, May 06 2015
%C An additional restriction is that a number is not a DPHP if it appears as the result as a product in any home prime search. So 25 is not a DPHP because a(10) => 2*5->25 => 5*11->511 => 7*73->773, and 25 appears in the process. - _Dana Jacobsen_, May 23 2015
%C 49 and 77 do not currently have known home prime sequences, hence it is unknown if they are in the DPHP sequence. - _Dana Jacobsen_, May 06 2015
%D Jeffrey Heleen, Family Numbers: Mathemagical Black Holes, Recreational and Educational Computing, 5:5, pp. 6, 1990.
%D Jeffrey Heleen, Family numbers: Constructing Primes by Prime Factor Splicing, J. Recreational Math., Vol. 28 #2, 1996-97, pp. 116-119.
%H Patrick De Geest's World!Of Numbers, <a href="http://www.worldofnumbers.com/em194.htm">Wonplate 194</a>
%H Patrick De Geest's World!Of Numbers, <a href="http://www.worldofnumbers.com/topic1.htm">Home Primes</a>
%e Starting number 16 takes 4 iterations to get to the home prime of 31636373:
%e 16 -> 2 * 2 * 2 * 2;
%e 2222 -> 2 * 11 * 101;
%e 211101 -> 3 * 11 * 6397;
%e 3116397 -> 3 * 163 * 6373;
%e 31636373 -> prime.
%e Now take all the factors found, in order: 2222211101311639731636373, a prime.
%e So 16 leads to a DPHP.
%Y Cf. A037274.
%K nonn,base,more
%O 1,1
%A _Jeff Heleen_, Apr 26 2015
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