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A038615 Primes not containing the digit '7'. 23
2, 3, 5, 11, 13, 19, 23, 29, 31, 41, 43, 53, 59, 61, 83, 89, 101, 103, 109, 113, 131, 139, 149, 151, 163, 181, 191, 193, 199, 211, 223, 229, 233, 239, 241, 251, 263, 269, 281, 283, 293, 311, 313, 331, 349, 353, 359, 383, 389, 401, 409, 419, 421, 431, 433, 439 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Subsequence of primes of A052419. - Michel Marcus, Feb 22 2015
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
LINKS
Marianne Freiberger, Primes without 7s, +plus magazine, August 2016.
M. F. Hasler, Numbers avoiding certain digits, OEIS wiki, Jan 12 2020.
James Maynard, Primes with restricted digits, arXiv:1604.01041 [math.NT], 2016.
James Maynard and Brady Haran, Primes without a 7, Numberphile video (2019).
FORMULA
Intersection of A000040 (primes) and A052419 (numbers with no digit 7). - M. F. Hasler, Jan 11 2020
a(n) ~ n^(log 10/log 9) log n. - Charles R Greathouse IV, Aug 03 2023
MATHEMATICA
Select[Prime[Range[70]], DigitCount[#, 10, 7] == 0 &] (* Vincenzo Librandi, Aug 08 2011 *)
PROG
(Magma) [ p: p in PrimesUpTo(500) | not 7 in Intseq(p) ]; // Bruno Berselli, Aug 08 2011
(PARI) lista(nn)=forprime(p=2, nn, if (!vecsearch(vecsort(digits(p), , 8), 7), print1(p, ", ")); ); \\ Michel Marcus, Feb 22 2015
(PARI) (A038615_upto(N)=select( is_A052419, primes([1, N])))(444) \\ i.e.: {is_A038615(n)=is_A052419(n)&&isprime(n)}; {is_A052419(n)=!setsearch(Set(digits(n)), 7)}. - M. F. Hasler, Jan 11 2020
CROSSREFS
Primes having no digit d = 0..9 are A038618, A038603, A038604, A038611, A038612, A038613, A038614, this sequence, A038616, and A038617, respectively.
Sequence in context: A184859 A193213 A153135 * A280930 A104293 A153002
KEYWORD
nonn,easy,base
AUTHOR
Vasiliy Danilov (danilovv(AT)usa.net), Jul 15 1998
EXTENSIONS
Offset corrected by Arkadiusz Wesolowski, Aug 07 2011
STATUS
approved

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Last modified March 28 10:55 EDT 2024. Contains 371241 sequences. (Running on oeis4.)