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 A257496 Doubly prime home primes (DPHP). 0
 9, 16, 26, 42 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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. Further terms are 74, 75, 95. 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 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 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 REFERENCES Jeffrey Heleen, Family Numbers: Mathemagical Black Holes, Recreational and Educational Computing, 5:5, pp. 6, 1990. Jeffrey Heleen, Family numbers: Constructing Primes by Prime Factor Splicing, J. Recreational Math., Vol. 28 #2, 1996-97, pp. 116-119. LINKS Patrick De Geest's World!Of Numbers, Wonplate 194 Patrick De Geest's World!Of Numbers, Home Primes EXAMPLE Starting number 16 takes 4 iterations to get to the home prime of 31636373: 16 -> 2 * 2 * 2 * 2; 2222 -> 2 * 11 * 101; 211101 -> 3 * 11 * 6397; 3116397 -> 3 * 163 * 6373; 31636373 -> prime. Now take all the factors found, in order: 2222211101311639731636373, a prime. So 16 leads to a DPHP. CROSSREFS Cf. A037274. Sequence in context: A161183 A183345 A048752 * A162616 A153362 A039788 Adjacent sequences:  A257493 A257494 A257495 * A257497 A257498 A257499 KEYWORD nonn,base,more AUTHOR Jeff Heleen, Apr 26 2015 STATUS approved

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