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
KEYWORD
nonn,base,easy,nice
AUTHOR
EXTENSIONS
More terms from Erich Friedman
STATUS
approved