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A141389
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a(n) = successive rank in A000040 of primes deleted from the working sequence according to their rank in that sequence equal to the digital root of the value of the previous deleted prime. The working sequence is A000040 deprived progressively of these deleted terms.
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0
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2, 4, 9, 7, 12, 1, 5, 6, 11, 13, 15, 8, 3, 18, 21, 10, 16, 25, 24, 27, 20, 29, 14, 30, 26, 19, 28, 35, 32, 33, 22, 38, 17, 37, 36, 42, 23, 34, 41, 47, 43, 39, 46, 31, 40, 45, 54, 55, 51, 57, 58, 44, 52, 56, 49, 50, 60, 53, 65, 66, 59, 68, 63, 48, 71, 62, 70, 74, 69, 73, 77, 64, 76, 78, 61, 79, 81, 82, 85, 86
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OFFSET
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1,1
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COMMENTS
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If, as seems quite probable, all the digits 1 to 9 are infinitely repeated in the sequence of natural roots of prime numbers, all the terms of A000040 are progressively deleted, hence the sequence should be a permutation of the natural numbers.
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LINKS
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FORMULA
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The digital root of A000040(1)=P(1) is 2, so we delete from this sequence p(2)=3 and assign the value 2 to a(1).
The digital root of the first term deleted is 3, so the second term we delete from the working sequence is the third one, i.e., 7, whose rank in A000040 is 4. Hence a(2)=4.
The digital root of the second term deleted is 7, so we delete from the working sequence its 7th term, i.e., 23, whose rank in A000040 is 9; hence a(3)=9; and so forth.
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EXAMPLE
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The digital root of the 3rd term deleted (23) is 5, so we delete from the working sequence the 5th term, i.e., 17, whose rank in A000040 is 7, which is the value that we assign to a(4).
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MATHEMATICA
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nmax=80; Clear[a, p, w]; dr[n_] := 1 + Mod[n-1, 9]; w[0] = Prime /@ Range[2nmax]; p[0]=2; a[n_] := (w[n] = DeleteCases[w[n-1], p[n] = w[n-1][[dr[p[n-1]]]]]; PrimePi[p[n]]); Table[a[n], {n, 1, nmax}] (* Jean-François Alcover, Aug 11 2017 *)
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CROSSREFS
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KEYWORD
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base,easy,nonn
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AUTHOR
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Philippe Lallouet (philip.lallouet(AT)orange.fr), Aug 03 2008
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EXTENSIONS
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STATUS
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approved
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