A208241 - OEIS

A208241

Smallest prime greater than n, with n as prefix in binary representation.

2, 5, 7, 17, 11, 13, 29, 17, 19, 41, 23, 97, 53, 29, 31, 67, 71, 37, 79, 41, 43, 89, 47, 97, 101, 53, 109, 113, 59, 61, 127, 131, 67, 137, 71, 73, 149, 307, 79, 163, 83, 337, 173, 89, 181, 373, 191, 97, 197, 101, 103, 211, 107, 109, 223, 113, 229, 233, 239

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

A208238(n) <= a(n);

A174332(n) = a(A000040(n)).

LINKS

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

MAPLE

A208241 := proc(n)

local nbin, len, suf, sufbin, pbin, p ;

nbin := convert(n, base, 2) ;

for len from 1 do

for suf from 0 to 2^len-1 do

sufbin := convert(suf, base, 2) ;

while nops(sufbin) < len do

sufbin := [op(sufbin), 0] ;

end do:

pbin := [op(sufbin), op(nbin)] ;

p := add( 2^(i-1)*op(i, pbin), i=1..nops(pbin) ) ;

if isprime(p) then

return p ;

end if;

end do:

end proc:

seq(A208241(n), n=1..50) ; # R. J. Mathar, May 06 2017

PROG

(Haskell)

import Data.List (genericIndex, find, isPrefixOf)

import Data.Maybe (fromJust)

a208241 = genericIndex a208241_list

a208241_list = f nns $ filter ((== 1) . a010051' . fst) nns where

f mms'@((m, ms):mms) pps'@((p, ps):pps) =

if m == p then f mms' pps else q : f mms pps'

where q = fst $ fromJust $ find ((ms `isPrefixOf`) . snd) pps'

nns = zip [1..] $ map reverse $ tail a030308_tabf

CROSSREFS

Cf. A208238, A004676, A007088, A010051, A030308, A055011 (iterated).

Cf. A164022 (greater or equal).

Sequence in context: A181447 A082088 A075881 * A089727 A113514 A145674

Adjacent sequences: A208238 A208239 A208240 * A208242 A208243 A208244

KEYWORD

nonn,base

AUTHOR

Reinhard Zumkeller, Feb 14 2013

STATUS

approved