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A038604
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Primes not containing the digit '2'.
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13
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3, 5, 7, 11, 13, 17, 19, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397
(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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Maynard proves that this sequence is infinite and in particular contains the expected number of elements up to x, on the order of x^(log 9/log 10)/log x. - Charles R Greathouse IV, Apr 08 2016
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LINKS
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FORMULA
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MATHEMATICA
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Select[Prime[Range[70]], DigitCount[#, 10, 2] == 0 &] (* Vincenzo Librandi, Aug 08 2011 *)
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PROG
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(Magma) [ p: p in PrimesUpTo(400) | not 2 in Intseq(p) ]; // Bruno Berselli, Aug 08 2011
(PARI) lista(nn, d=2) = {forprime(p=2, nn, if (!vecsearch(vecsort(digits(p), , 8), d), print1(p, ", ")); ); } \\ Michel Marcus, Feb 21 2015
(PARI)
select( {is_A038604(n)=is_A052404(n)&&isprime(n)}, [1..400]) \\ see Wiki for more
(Python)
from sympy import isprime, nextprime
def is_A038604(n): return str(n).find('2')<0 and isprime(n)
def next_A038604(n): # get smallest term > n
while True:
n = nextprime(n); s = str(n); t = s.find('2')
if t < 0: return n
t = 10**(len(s)-1-t); n += t - n%t
def A038604_upto(stop=math.inf, start=3):
while start < stop: yield start; start = next_A038604(start)
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CROSSREFS
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Subsequence of A065091 (odd primes).
Primes having no digit d = 0..9 are A038618, A038603, this sequence, A038611, A038612, A038613, A038614, A038615, A038616, and A038617, respectively.
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KEYWORD
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nonn,easy,base
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AUTHOR
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Vasiliy Danilov (danilovv(AT)usa.net), Jul 15 1998
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EXTENSIONS
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STATUS
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approved
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