

A257496


Doubly prime home primes (DPHP).


0




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, 199697, pp. 116119.


LINKS

Table of n, a(n) for n=1..4.
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: A183345 A303873 A048752 * A162616 A153362 A039788
Adjacent sequences: A257493 A257494 A257495 * A257497 A257498 A257499


KEYWORD

nonn,base,more


AUTHOR

Jeff Heleen, Apr 26 2015


STATUS

approved



