A033664 Every suffix is prime.

2, 3, 5, 7, 13, 17, 23, 37, 43, 47, 53, 67, 73, 83, 97, 103, 107, 113, 137, 167, 173, 197, 223, 283, 307, 313, 317, 337, 347, 353, 367, 373, 383, 397, 443, 467, 503, 523, 547, 607, 613, 617, 643, 647, 653, 673, 683, 743, 773, 797, 823, 853, 883, 907, 937, 947

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• base
• easy
• nice

Comments

Primes in which repeatedly deleting the most significant digit gives a prime at every step until a single-digit prime remains.

Every digit string containing the least significant digit is prime. - Amarnath Murthy, Sep 24 2003

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..66973 (first 8779 terms from T. D. Noe)
• Eric Weisstein's World of Mathematics, Truncatable Prime.

Crossrefs

Cf. A024785, A032437, A020994, A024770, A052023, A052024, A052025, A050986, A050987, A069866, A038680, A010051, A000040.

Programs

Haskell

a033664 n = a033664_list !! (n-1)
a033664_list = filter (all ((== 1) . a010051. read) .
                           init . tail . tails . show) a000040_list
-- Reinhard Zumkeller, Jul 10 2013

Maple

T:= proc(n) option remember; `if`(n=0, "", select(isprime, [seq(seq(
      seq(parse(cat(j, 0$(n-i), p)), p=[T(i-1)]), i=1..n), j=1..9)])[])
    end:
seq(T(n), n=1..4);  # Alois P. Heinz, Sep 01 2021

Mathematica

h8pQ[n_]:=And@@PrimeQ/@Most[NestWhileList[FromDigits[Rest[ IntegerDigits[ #]]]&, n,#>0&]]; Select[Prime[Range[1000]],h8pQ] (* Harvey P. Dale, May 26 2011 *)

PARI

fileO="b033664.txt";lim=8779;v=vector(lim);v[1]=2;v[2]=3;v[3]=5;v[4]=7;j=4; write(fileO,"1 2");write(fileO,"2 3");write(fileO,"3 5");write(fileO,"4 7"); p10=1;until(0,p10*=10;j0=j;for(k=1,9,k10=k*p10; for(i=1,j0,if(j==lim,break(3));z=k10+v[i]; if(isprime(z),j++;v[j]=z;write(fileO,j," ",z);)))) \\ Harry J. Smith, Sep 20 2008

Python

from sympy import isprime, primerange
def ok(p): # does prime p satisfy the property
    s = str(p)
    return all(isprime(int(s[i:])) for i in range(1, len(s)))
print(list(filter(ok, primerange(1, 1000)))) # Michael S. Branicky, Sep 01 2021

Python

# alternate for going to large numbers
def agen(maxdigits):
    yield from [2, 3, 5, 7]
    primestrs, digits, d = ["2", "3", "5", "7"], "0123456789", 1
    while len(primestrs) > 0 and d < maxdigits:
        cands = set(d+p for p in primestrs for d in "0123456789")
        primestrs = [c for c in cands if c[0] == "0" or isprime(int(c))]
        yield from sorted(map(int, (p for p in primestrs if p[0] != "0")))
        d += 1
print([p for p in agen(11)]) # Michael S. Branicky, Sep 01 2021

Extensions

More terms from Erich Friedman