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A078834 Greatest prime factor of n also contained as binary substring in binary representation of n; a(n)=1, if no such factor exists. 3
1, 2, 3, 2, 5, 3, 7, 2, 1, 5, 11, 3, 13, 7, 3, 2, 17, 2, 19, 5, 1, 11, 23, 3, 1, 13, 3, 7, 29, 3, 31, 2, 1, 17, 1, 2, 37, 19, 3, 5, 41, 2, 43, 11, 5, 23, 47, 3, 1, 2, 3, 13, 53, 3, 11, 7, 3, 29, 59, 3, 61, 31, 7, 2, 1, 2, 67, 17, 1, 2, 71, 2, 73, 37, 5, 19, 1, 3, 79, 5, 1, 41, 83, 2, 5, 43 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) <= min{A078833(n), A006530(n)};

for n>1: a(n) = n iff n is prime.

a(A100484(n)) = A000040(n); a(A100368(n)) = A006530(A100368(n)). [Reinhard Zumkeller, Sep 19 2011]

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

EXAMPLE

n=15=3*5 has two factors; only '11'=3 is contained in '1111'=15, therefore a(15)=3.

MAPLE

with(numtheory): P:=proc(n) local a, b, c, k; a:=factorset(n);

b:=1; c:=convert(convert(n, binary, decimal), string);

for k from nops(a) by -1 to 1 do

if searchtext(convert(convert(a[k], binary, decimal), string), c)>0

then b:=a[k]; break; fi; od; b; end: seq(P(i), i=1..86);

# Paolo P. Lava, Nov 15 2018

MATHEMATICA

a[n_] := Module[{bn, pp, sel}, bn = IntegerDigits[n, 2]; pp = FactorInteger[n][[All, 1]]; sel = Select[pp, MatchQ[bn, {___, Sequence @@ IntegerDigits[#, 2], ___}] &]; If[sel == {}, 1, Max[sel]]]; Table[a[n], {n, 1, 100}] (* Jean-Fran├žois Alcover, Aug 13 2013 *)

PROG

(Haskell)

import Numeric (showIntAtBase)

import Data.List (find, isInfixOf)

import Data.Maybe (fromMaybe)

a078834 n = fromMaybe 1 $ find (\p -> showIntAtBase 2 ("01" !!) p ""

                          `isInfixOf` showIntAtBase 2 ("01" !!) n "") $

                 reverse $ a027748_row n

-- Reinhard Zumkeller, Sep 19 2011

CROSSREFS

Cf. A078833, A078822, A007088, A006530.

Sequence in context: A086281 A097975 A130088 * A039634 A078833 A210437

Adjacent sequences:  A078831 A078832 A078833 * A078835 A078836 A078837

KEYWORD

nonn,base,nice

AUTHOR

Reinhard Zumkeller, Dec 08 2002

STATUS

approved

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Last modified October 16 13:51 EDT 2019. Contains 328093 sequences. (Running on oeis4.)