A226229 Numbers m such that all lengths of runs of digits in base 2 representation of m are primes.

3, 7, 12, 24, 28, 31, 51, 56, 96, 99, 103, 115, 124, 127, 199, 204, 224, 227, 231, 248, 384, 387, 396, 408, 412, 415, 455, 460, 499, 508, 775, 792, 796, 799, 819, 824, 896, 899, 908, 920, 924, 927, 992, 995, 999, 1016, 1539, 1548, 1587, 1592, 1632, 1635, 1639, 1651, 1660

Offset: 1

Author

Alex Ratushnyak, May 31 2013

Keywords

• nonn
• base

Comments

Intersection of A226227 and A226228.

From Emeric Deutsch, Jan 27 2018: (Start)

Also the indices of the compositions having only prime parts. For the definition of the index of a composition see A298644. For example, 387 is in the sequence since its binary form is 110000011 and the parts of the composition [2,5,2] are prime numbers. 540 is not in the sequence since its binary form is 1000011100 and not all the parts of the composition [1,4,3,2] are primes.

The command c(n) from the Maple program yields the composition having index n. (End)

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A033015, A226227, A226228.

Cf. A005811, A030308, A010051.

Programs

Haskell

import Data.List (group, genericLength)
a226229 n = a226229_list !! (n-1)
a226229_list = filter
   (all (== 1) . map (a010051 . genericLength) . group . a030308_row) [1..]
-- Reinhard Zumkeller, Jun 05 2013

Maple

Runs := proc (L) local j, r, i, k: npr: j := 1; r[j] := L[1]: for i from 2 to nops(L) do if L[i] = L[i-1] then r[j] := r[j], L[i] else j := j+1: r[j] := L[i] end if end do: [seq([r[k]], k = 1 .. j)] end proc: RunLengths := proc (L) map(nops, Runs(L)) end proc: c := proc (n) ListTools:-Reverse(convert(n, base, 2)): RunLengths(%) end proc: npr := proc (s) local q, j: q := 0: for j to nops(s) do if isprime(s[j]) = true then q := q+1 else  end if end do end proc: A := {}: for n to 1661 do if npr(c(n)) = nops(c(n)) then A := `union`(A, {n}) else  end if end do: A; # most of the Maple program is due to W. Edwin Clark. # Emeric Deutsch, Jan 27 2018

Mathematica

Select[Range@1660, And @@ PrimeQ[Length /@ Split@ IntegerDigits[#, 2]] &] (* Giovanni Resta, Jun 01 2013 *)