A038615 Primes not containing the digit '7'.

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

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

Alois P. Heinz, Table of n, a(n) for n = 1..20000

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

Cf. A000040, A052419.

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

Adjacent sequences: A038612 A038613 A038614 * A038616 A038617 A038618

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