A094934 - OEIS

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A094934

Write binary digits of numbers 1, 2, 3, ... in a string; sequence gives the prime indexed digits.

1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0

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OFFSET

0,1

LINKS

Table of n, a(n) for n=0..104.

EXAMPLE

In 1 10 11 100 101 110 111 1000 ... the prime indexed digits are 1,0,1,0,1,1,1,0

MATHEMATICA

almostNatural[n_, b_] := Block[{m = 0, d = n, i = 1, l, p}, While[m <= d, l = m; m = (b - 1) i*b^(i - 1) + l; i++]; i--; p = Mod[d - l, i]; q = Floor[(d - l)/i] + b^(i - 1); If[p != 0, IntegerDigits[q, b][[p]], Mod[q - 1, b]]]; Table[ almostNatural[n, 2], {n, Prime@ Range@ 105}] (* Robert G. Wilson v, Jun 29 2014 *)

PROG

(PARI) { x=1; xlc=0; xl=0; forprime (p=2, 1000, fl=1; if (xlc>=p && xlc-xl<p, fl=0; print1(", "xb[p-xlc+xl])); while (fl==1, xb=binary(x); xl=length(xb); xlc+=xl; if (xlc>=p && xlc-xl<p, fl=0; print1(", "xb[p-xlc+xl])); x++)) }

CROSSREFS

Cf. A007376, A033307, A113566.

Sequence in context: A114607 A123110 A004593 * A245837 A245656 A354032

Adjacent sequences: A094931 A094932 A094933 * A094935 A094936 A094937

KEYWORD

nonn,base

AUTHOR

Jon Perry, Jun 17 2004

STATUS

approved