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A033664
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Every suffix is prime.
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21
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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
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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MAPLE
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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:
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MATHEMATICA
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h8pQ[n_]:=And@@PrimeQ/@Most[NestWhileList[FromDigits[Rest[ IntegerDigits[ #]]]&, n, #>0&]]; Select[Prime[Range[1000]], h8pQ] (* Harvey P. Dale, May 26 2011 *)
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PROG
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(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
(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)))
(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
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CROSSREFS
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Cf. A024785, A032437, A020994, A024770, A052023, A052024, A052025, A050986, A050987, A069866, A038680, A010051, A000040.
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KEYWORD
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nonn,base,easy,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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