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Search: id:A166849
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| A166849 |
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Primes with digital root 1, 2, 4 or 8. |
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+0
1
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| 2, 11, 13, 17, 19, 29, 31, 37, 47, 53, 67, 71, 73, 83, 89, 101, 103, 107, 109, 127, 137, 139, 157, 163, 173, 179, 181, 191, 193, 197, 199, 211, 227, 229, 233, 251, 263, 269, 271, 281, 283, 307, 317, 337, 353, 359, 373, 379, 389, 397, 409
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Primes which under repeated summation of digits eventually reach 1, 2, 4 or 8.
One might introduce the overall classification of the entire set of prime numbers, based on the outcome of calculating their digital roots (also called repeated digital sum - see http://en.wikipedia.org/wiki/Digital_root) Such classification yields four distinct classes of primes: a) powers of 2 (1, 2, 4, 8) - this sequence b) 3 - just one occurence c) 5 d) 7 Zak Seidov in private communication contributed the following computation/info: Among first 10^6 primes, the frequency of distribution of cases dig root = 1,2,3,4,5,7,8 is: {166568, 166751, 1, 166637, 166707, 166624, 166712} - uniform distribution with a great accuracy (except for 3 of course). [From Alexander R. Povolotsky (pevnev(AT)juno.com), Oct 23 2009] - More terms a(11)-a(51) from Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Oct 24 2009
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EXAMPLE
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The prime 229 is a member since 229 -> 13 -> 4.
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CROSSREFS
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Cf. A010888.
Sequence in context: A048521 A058048 A038915 this_sequence A119449 A158204 A137977
Adjacent sequences: A166846 A166847 A166848 this_sequence A166850 A166851 A166852
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KEYWORD
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nonn,base
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AUTHOR
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Alexander R. Povolotsky (pevnev(AT)juno.com), Oct 21 2009
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EXTENSIONS
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Edited by N. J. A. Sloane and Zak Seidov, Oct 23 2009
More terms a(11)-a(51) from Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Oct 24 2009
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