A090080 In binary expansion of n-th prime: reduce contiguous blocks of 0's to 0 and contiguous blocks of 1's to 1.

2, 1, 5, 1, 5, 5, 5, 5, 5, 5, 1, 21, 21, 21, 5, 21, 5, 5, 5, 5, 21, 5, 21, 21, 5, 21, 5, 21, 21, 5, 1, 5, 21, 21, 85, 21, 21, 21, 21, 85, 21, 85, 5, 5, 21, 5, 21, 5, 5, 21, 21, 5, 5, 5, 5, 5, 21, 5, 85, 21, 21, 85, 21, 21, 21, 21, 85, 85, 85, 85, 21, 21, 21, 85, 21, 5, 21, 21, 21

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

a(n) = A090079(A000040(n)).

Example

A000040(25)=97 -> '1100001' -> [11][0000][1] -> [1][0][1] ->
'101' -> 5=a(25).

Maple

f:= proc(n) local L, k;
  L:= convert(n, base, 2);
  k:= 1+numboccur(1, L[1..-2]-L[2..-1]);
  (4^k-1)/3
end proc:
f(2):= 2:
map(f @ ithprime, [$1..100]); # Robert Israel, Jun 05 2026

Mathematica

A090080[n_] := FromDigits[DeleteAdjacentDuplicates[IntegerDigits[Prime[n], 2]], 2];
Array[A090080, 100] (* Paolo Xausa, Jun 06 2026 *)

Crossrefs

Cf. A000040, A004676, A090079.

Sequence in context: A379654 A060448 A378543 * A151737 A211361 A347464

Adjacent sequences: A090077 A090078 A090079 * A090081 A090082 A090083

Keyword

nonn,base,changed

Author

Reinhard Zumkeller, Nov 20 2003

Status

approved