A067600 Numbers n such that f(n) and f(f(n)) are prime, where f(k) = decimal encoding of the prime factorization of k.

3, 20, 69, 171, 174, 267, 333, 360, 372, 448, 537, 665, 666, 776, 820, 824, 855, 873, 1016, 1125, 1330, 1413, 1450, 1532, 1604, 1689, 1796, 1860, 1899, 1959, 2048, 2068, 2184, 2319, 2449, 2620, 2658, 2670, 2804, 2823, 3139, 3210, 3342, 3464, 3552, 3589

Offset

1,1

Comments

If n = p_1^e_1 * ... * p_r^e_r with p_1 < ... < p_r, then its decimal encoding is p_1 e_1...p_r e_r. For example, 15 = 3^1 * 5^1, so has decimal encoding 3151.

Links

Table of n, a(n) for n=1..46.

Example

The prime factorization of 20 = 2^2 * 5^1 with corresponding encoding 2251, which is a prime. 2251 = 2251^1 has encoding 22511, which is also prime. So 20 is a term of the sequence.

Mathematica

f[n_] := FromDigits[Flatten[IntegerDigits[FactorInteger[n]]]]; Select[ Range[4000], Union[ PrimeQ[ Drop[ NestList[f, #, 2], 1]]] == {True} & ]

Crossrefs

Cf. A067599.

Sequence in context: A345689 A292072 A183377 * A348208 A160456 A289643

Adjacent sequences: A067597 A067598 A067599 * A067601 A067602 A067603

Keyword

base,easy,nonn

Author

Joseph L. Pe, Jan 31 2002

Extensions

Edited by Robert G. Wilson v and N. J. A. Sloane, Feb 02 2002

Status

approved