cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A226229 #21 Jan 28 2018 17:38:19
%S A226229 3,7,12,24,28,31,51,56,96,99,103,115,124,127,199,204,224,227,231,248,
%T A226229 384,387,396,408,412,415,455,460,499,508,775,792,796,799,819,824,896,
%U A226229 899,908,920,924,927,992,995,999,1016,1539,1548,1587,1592,1632,1635,1639,1651,1660
%N A226229 Numbers m such that all lengths of runs of digits in base 2 representation of m are primes.
%C A226229 Intersection of A226227 and A226228.
%C A226229 From _Emeric Deutsch_, Jan 27 2018: (Start)
%C A226229 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.
%C A226229 The command c(n) from the Maple program yields the composition having index n. (End)
%H A226229 Reinhard Zumkeller, <a href="/A226229/b226229.txt">Table of n, a(n) for n = 1..1000</a>
%p A226229 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
%t A226229 Select[Range@1660, And @@ PrimeQ[Length /@ Split@ IntegerDigits[#, 2]] &] (* _Giovanni Resta_, Jun 01 2013 *)
%o A226229 (Haskell)
%o A226229 import Data.List (group, genericLength)
%o A226229 a226229 n = a226229_list !! (n-1)
%o A226229 a226229_list = filter
%o A226229    (all (== 1) . map (a010051 . genericLength) . group . a030308_row) [1..]
%o A226229 -- _Reinhard Zumkeller_, Jun 05 2013
%Y A226229 Cf. A033015, A226227, A226228.
%Y A226229 Cf. A005811, A030308, A010051.
%K A226229 nonn,base
%O A226229 1,1
%A A226229 _Alex Ratushnyak_, May 31 2013