A069090 Primes none of whose proper initial segments are primes.

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

Offset: 1

Author

Joseph L. Pe, Apr 05 2002

Keywords

• base
• nonn

Examples

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

Links

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

Crossrefs

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

Cf. A000040, A010051, A276707.

Programs

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

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 *)

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

Python

from sympy import primerange, isprime
def ok(p):
    s = str(p)
    if len(s) == 1: return True
    return all(not isprime(int(s[:i])) for i in range(1, len(s)))
def aupto(lim):
    alst = []
    for p in primerange(1, lim+1):
        if ok(p): alst.append(p)
    return alst
print(aupto(829)) # Michael S. Branicky, Jul 03 2021

Extensions

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