A257496 Doubly prime home primes (DPHP).

9, 16, 26, 42

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

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: A161183 A183345 A303873 * A351435 A369642 A162616

Adjacent sequences: A257493 A257494 A257495 * A257497 A257498 A257499

Keyword

nonn,base,more

Author

Jeff Heleen, Apr 26 2015

Status

approved