A090724 Defined in Comments lines.

4, 1, 3, 5, 3, 4, 1, 3, 4, 1, 3, 5, 5, 2, 0, 5, 2, 4, 1, 6, 3, 3, 0, 6, 4, 2, 3, 5, 2, 3, 1, 4, 2, 3, 3, 5, 5, 2, 0, 3, 5, 3, 1, 3, 5, 3, 1, 6, 3, 1, 0, 5, 5, 2, 0, 5, 2, 4, 3, 5, 2, 4, 2, 3, 4, 3, 1, 6, 3, 3, 3, 4, 5, 2, 2, 3, 3, 2, 0, 3, 5, 2, 3, 4, 4, 1, 3, 5, 3, 3, 0, 4, 5, 2, 0, 6, 2, 3, 2, 6, 3, 1, 2, 5, 5

Offset: 4

Author

Roger L. Bagula, Jan 18 2004

Keywords

• nonn
• base
• less

Comments

1. Start with the sequence of final digits of primes (A007652), beginning at 7 so that all members of this sequence will be either 1,3,7, or 9: {7,1,3,7,9,3,9,1,7,1,3,7,3,9,1,7,1,3,...}.

2. Replace all 3's with 6's, all 1's with 3's, all 7's with 5's and all 9's with 4's: {5,3,6,5,4,6,4,3,5,3,6,5,6,4,3,5,3,6, ...}.

3. Subtract (n mod 4) from the n-th member of this sequence (i.e. subtract 1 from the first, 5th, 9th, 13th, ... members, subtract 2 from the 2nd, 6th, 10th, ... members and subtract 3 from the 3rd, 7th, 11th,... members) to get the final sequence: {4,1,3,5,3,4,1,3,4,1,3,5,5,2,0,5,2,4, ...}.

The {0,1,2,3,4,5,6} symbols coded onto the modulo 4 cycle {1,2,3,4} by the prime digits set {1,3,7,9}.

Programs

Mathematica

ReplaceAll[Table[Mod[Prime[n+3], 10], {n, 200}], {1->3, 3->6, 7->5, 9->4}]-Table[Mod[n, 4], {n, 200}]