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A069090 Primes none of whose proper initial segments are primes. 4
2, 3, 5, 7, 11, 13, 17, 19, 41, 43, 47, 61, 67, 83, 89, 97, 101, 103, 107, 109, 127, 149, 151, 157, 163, 167, 181, 401, 409, 421, 443, 449, 457, 461, 463, 467, 487, 491, 499, 601, 607, 631, 641, 643, 647, 653, 659, 661, 683, 691, 809, 811, 821, 823, 827, 829 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Franklin T. Adams-Watters and R. Zumkeller, Table of n, a(n) for n = 1..10000 Initial 1000 terms by Franklin T. Adams-Watters

Barry Carter, Table of n, a(n) for n = 1..1411151 (bz2 compressed)

Barry Carter, Mathematica program

StackExchange, Number of digits until a prime is reached

EXAMPLE

The proper initial segments of 499 are 4 and 49, none of which are primes. So 499 is a term of the sequence.

MAPLE

isA069090 := proc(n)

    local dgs, l ;

    if isprime(n) then

        dgs := convert(n, base, 10) ;

        ndgs := nops(dgs) ;

        for l from 1 to ndgs-1 do

            add( op(ndgs+i-l+1, dgs)*10^i, i=0..l-1) ;

            if isprime(%) then

                return false;

            end if;

        end do:

        true ;

    else

        false ;

    end if;

end proc:

for n from 2 to 830 do

    if isA069090(n) then

        printf("%d, ", n);

    end if;

end do: # R. J. Mathar, Dec 15 2016

MATHEMATICA

Select[Prime[Range[200]], NoneTrue[FromDigits/@Table[Take[ IntegerDigits[ #], n], {n, IntegerLength[#]-1}], PrimeQ]&] (* The program uses the NoneTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jul 24 2016 *)

PROG

(PARI) ina(n)=if(!isprime(n), return(0)); while(n>9, n\=10; if(isprime(n), return(0))); 1 \\ Franklin T. Adams-Watters, Jun 26 2009

(Haskell)

import Data.List (inits)

a069090 n = a069090_list !! (n-1)

a069090_list = filter

   (all (== 0) . map (a010051 . read) . init . tail . inits . show)

   a000040_list

-- Reinhard Zumkeller, Mar 11 2014

CROSSREFS

Cf. A074721. [Franklin T. Adams-Watters, Jun 26 2009]

Cf. A000040, A010051.

Sequence in context: A216496 A069709 A144755 * A088415 A175063 A248199

Adjacent sequences:  A069087 A069088 A069089 * A069091 A069092 A069093

KEYWORD

base,nonn

AUTHOR

Joseph L. Pe, Apr 05 2002

EXTENSIONS

More terms from Franklin T. Adams-Watters, Jun 26 2009

STATUS

approved

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Last modified June 22 12:17 EDT 2017. Contains 288613 sequences.