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A072003
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10's complement of final digit of n-th prime.
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2
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8, 7, 5, 3, 9, 7, 3, 1, 7, 1, 9, 3, 9, 7, 3, 7, 1, 9, 3, 9, 7, 1, 7, 1, 3, 9, 7, 3, 1, 7, 3, 9, 3, 1, 1, 9, 3, 7, 3, 7, 1, 9, 9, 7, 3, 1, 9, 7, 3, 1, 7, 1, 9, 9, 3, 7, 1, 9, 3, 9, 7, 7, 3, 9, 7, 3, 9, 3, 3, 1, 7, 1, 3, 7, 1, 7, 1, 3, 9, 1, 1, 9, 9, 7, 1, 7, 1, 3, 9, 7, 3, 1, 3, 9, 1, 7, 1, 9, 7, 9, 3, 3, 7, 1, 9
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| If the first, second and third terms are omitted and the result is taken as a fractional part, the result is what I call a pseudorational number. The set {1,3,7,9} form a multiplicative group modulo 10 and the resulting table is also a magic square with sum 20.
After the first 8,7,5 preface the sequence is all 1,3,7,9 and the group in multiplication makes them "orthogonal" as the magic square of the modulo 10 multiplication table shows. The Beatty bi infinite word for the pseudorandom is five letters long in its repeating form. The result is to break the primes into six sets, two of which have only one element and the others four form groups that are chaotic, but orthogonal to each other.
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FORMULA
| a(n) = 10 - Prime(n) (Mod 10)
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EXAMPLE
| 10-mod[2,10]=8 10-mod[3,10]=7 10-mod[5,10]=5 10-mod[7,10]=3 10-mod[11,10]=1 etc.
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MATHEMATICA
| a[n_] := 10-mod[Prime[n], 10]; Table[ a[n], {n, 1, 105}]
(* Pseudorational number generated is: *) N[ Sum[ a[n]^10*(-n+3), {n, 4, 200}], 198]
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CROSSREFS
| Cf. A007652(n)+A072003(n) = 10.
Sequence in context: A076417 A114137 A200017 * A160668 A086033 A195846
Adjacent sequences: A072000 A072001 A072002 * A072004 A072005 A072006
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KEYWORD
| nonn,base
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jun 18 2002
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com) and Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 20 2002
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