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A181642 Minimal sequence whose forwards Van Eck transform is the sequence of prime numbers. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

At each step, the minimum available integer is used.

From Rémy Sigrist, Aug 12 2017: (Start)

a(n)=0 iff n belongs to A074271.

a(n)=1 iff n > 1 and n belongs to A259408.

For any k > 0, A064427(k) = least n such that a(n) = k-1.

(End)

LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..10000

EXAMPLE

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.

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);

PROG

(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

CROSSREFS

Cf. A000040, A064427, A074271, A181391, A259408.

Sequence in context: A061413 A286385 A074743 * A011358 A160188 A322081

Adjacent sequences:  A181639 A181640 A181641 * A181643 A181644 A181645

KEYWORD

easy,nonn

AUTHOR

Paolo P. Lava & Giorgio Balzarotti, Nov 03 2010

EXTENSIONS

More terms from Rémy Sigrist, Aug 12 2017

STATUS

approved

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Last modified May 26 22:16 EDT 2019. Contains 323597 sequences. (Running on oeis4.)