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

1,1

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

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
(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

Crossrefs

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

Cf. A000040, A010051, A276707.

Sequence in context: A216496 A069709 A144755 * A321150 A088415 A175063

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