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Search: id:A067600
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| A067600 |
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Numbers n such that f(n) and f(f(n)) are prime, where f(k) = decimal encoding of the prime factorization of k. |
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+0
2
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| 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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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.
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EXAMPLE
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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.
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MATHEMATICA
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f[n_] := FromDigits[Flatten[IntegerDigits[FactorInteger[n]]]]; Select[ Range[4000], Union[ PrimeQ[ Drop[ NestList[f, #, 2], 1]]] == {True} & ]
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CROSSREFS
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Cf. A067599.
Adjacent sequences: A067597 A067598 A067599 this_sequence A067601 A067602 A067603
Sequence in context: A062359 A099721 A024402 this_sequence A006411 A129549 A092786
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KEYWORD
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base,easy,nonn
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AUTHOR
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Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Jan 31 2002
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EXTENSIONS
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Edited by Robert G. Wilson v (rgwv(AT)rgwv.com) and njas, Feb 02 2002
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