A181642 Minimal sequence whose forwards van Eck transform is the sequence of prime numbers.
0, 1, 0, 2, 1, 3, 4, 0, 5, 6, 2, 7, 8, 9, 10, 1, 11, 12, 3, 13, 14, 15, 16, 4, 17, 18, 0, 19, 20, 21, 22, 5, 23, 24, 25, 26, 27, 28, 6, 29, 30, 2, 31, 32, 33, 34, 35, 36, 7, 37, 38, 39, 40, 8, 41, 42, 9, 43, 44, 45, 46, 10, 47, 48, 49, 50, 51, 52, 1, 53, 54
Offset: 1
Examples
a(1)=0. Next 0 is at distance 2 (1st prime): a(3)=0. a(2)=1. Next 1 is at distance 3 (2nd prime): a(5)=1. a(3)=0. Next 0 is at distance 5 (3rd prime): a(8)=0. For a(4), we can use neither 0 (distance 1 from previous 0 would lead to an incongruence) nor 1 (distance 1 from subsequent 1 would lead to another incongruence). Therefore we must use 2. Next 2 must be at distance 7 (4th prime): a(11)=2. And so on.
Links
- Rémy Sigrist, Table of n, a(n) for n = 1..10000
Programs
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Maple
P:=proc(q,h) local i,k,n,t,x; x:=array(1..h); for k from 1 to h do x[k]:=-1; od; x[1]:=0; i:=0; t:=0;for n from 1 to q do if isprime(n) then i:=i+1; if x[i]>-1 then x[i+n]:=x[i]; else t:=t+1; x[i]:=t; x[i+n]:=x[i]; fi; fi; od; seq(x[k],k=1..79); end: P(400,500);
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PARI
a = vector(71, i, -1); u = 0; for (n=1, #a, if (a[n]<0, o = n; while (o <= #a, a[o] = u; o += prime(o)); u++); print1 (a[n] ", ")) \\ Rémy Sigrist, Aug 12 2017
Extensions
More terms from Rémy Sigrist, Aug 12 2017
Comments