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A072003 10's complement of final digit of n-th prime. 2
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; text; internal format)
OFFSET

1,1

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.

LINKS

Table of n, a(n) for n=1..105.

FORMULA

a(n) = 10 - Prime(n) (Mod 10)

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.

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]

CROSSREFS

Cf. A007652(n)+A072003(n) = 10.

Sequence in context: A200017 A316728 A231098 * A160668 A086033 A246504

Adjacent sequences:  A072000 A072001 A072002 * A072004 A072005 A072006

KEYWORD

nonn,base

AUTHOR

Roger L. Bagula, Jun 18 2002

EXTENSIONS

Edited by N. J. A. Sloane and Robert G. Wilson v, Jun 20 2002

STATUS

approved

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Last modified June 22 21:29 EDT 2021. Contains 345393 sequences. (Running on oeis4.)