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A226229 Numbers m such that all lengths of runs of digits in base 2 representation of m are primes. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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

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 *)

PROG

(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

CROSSREFS

Cf. A033015, A226227, A226228.

Cf. A005811, A030308, A010051.

Sequence in context: A243190 A256483 A262567 * A167491 A210185 A280345

Adjacent sequences:  A226226 A226227 A226228 * A226230 A226231 A226232

KEYWORD

nonn,base

AUTHOR

Alex Ratushnyak, May 31 2013

STATUS

approved

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Last modified May 31 02:51 EDT 2020. Contains 334747 sequences. (Running on oeis4.)