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

1,1

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.

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 *)

Prog

(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
(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
(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

Crossrefs

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

Sequence in context: A067905 A042993 A308711 * A024785 A069866 A125772

Adjacent sequences: A033661 A033662 A033663 * A033665 A033666 A033667

Keyword

nonn,base,easy,nice

Author

N. J. A. Sloane

Extensions

More terms from Erich Friedman

Status

approved