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 A038613 Primes not containing the digit '5'. 11
 2, 3, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 263, 269, 271, 277, 281, 283, 293, 307, 311 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Subsequence of primes of A052413. - 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 Table of n, a(n) for n=1..57. 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 a(n) ~ n^(log 10/log 9) log n. - Charles R Greathouse IV, Aug 03 2023 EXAMPLE From M. F. Hasler, Jan 14 2020: (Start) After a(85) = 499, the next prime without digit 5 is a(86) = 601. After a(3734) = 49999, the next term is a(3735) = 60013. After a(27273) = 499979, the next term is 600011. After a(206276) = 4999999, the next term is 6000011. (End) MATHEMATICA Select[Prime[Range[70]], DigitCount[#, 10, 5] == 0 &] (* Vincenzo Librandi, Aug 08 2011 *) PROG (Magma) [ p: p in PrimesUpTo(400) | not 5 in Intseq(p) ]; // Bruno Berselli, Aug 08 2011 (PARI) lista(nn)=forprime(p=2, nn, if (!vecsearch(vecsort(digits(p), , 8), 5), print1(p, ", ")); ); \\ Michel Marcus, Feb 22 2015 (A038613_upto(n)=select( is_A052413, primes([1, n])))(350) \\ see A052413 next_A038613(n)={until(isprime(n), n=next_A052413(nextprime(n+1)-1)); n} ( {A038613_vec(n, M=1)=M--; vector(n, i, M=next_A038613(M))} )(20, 1000) \\ Compute n terms >= M. See also the OEIS wiki page. - M. F. Hasler, Jan 14 2020 CROSSREFS Intersection of A000040 (primes) and A052413 (numbers with no digit 5). Primes having no digit d = 0..9 are A038618, A038603, A038604, A038611, A038612, this sequence, A038614, A038615, A038616, and A038617, respectively. Sequence in context: A088905 A045319 A178943 * A075235 A020634 A173555 Adjacent sequences: A038610 A038611 A038612 * A038614 A038615 A038616 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 December 1 15:49 EST 2023. Contains 367476 sequences. (Running on oeis4.)