A056709 Naught-y primes, primes with noughts (or zeros).

101, 103, 107, 109, 307, 401, 409, 503, 509, 601, 607, 701, 709, 809, 907, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1201, 1301, 1303, 1307, 1409, 1601, 1607, 1609, 1709, 1801, 1901, 1907

Offset

1,1

Comments

Intersection of A000040 and A011540. - Michel Marcus, Mar 12 2015

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Chris Caldwell, Naughty prime, Prime Pages' Glossary (UTM). (Date?)

Formula

a(n) ~ n log n: almost all primes are in this sequence. - Charles R Greathouse IV, Jul 24 2012

Mathematica

Select[ Range[ 1, 2500, 2 ], PrimeQ[ # ] && Sort[ RealDigits[ # ][ [ 1 ] ] ][ [ 1 ] ] == 0 & ]
(* Second program: *)
Select[Prime@ Range@ 300, DigitCount[#, 10, 0] > 0 &] (* Michael De Vlieger, Jan 28 2020 *)

Prog

(PARI) is(n)=isprime(n)&&vecsort(eval(Vec(Str(n))), , 8)[1]==0
(PARI)
select( {is_A056709(n)=!vecmin(digits(n))&&isprime(n)}, [1..2000]) \\ Defines the characteristic function is_A; as check & example: select terms in [1..2000].
next_A056709(n)={until(!vecmin(digits(n)), n=nextprime(n+1)); n} \\ Successor function: find smallest a(k) > n. Useful to get a vector of consecutive terms:
A056709_vec(n, M=99)=M--; vector(n, i, M=next_A056709(M)) \\ get n terms >= M (if given, else start with a(1)).  \\ M. F. Hasler, Jan 12 2020
(Magma) [p:p in PrimesUpTo(2000)|0 in Intseq(p)]; // Marius A. Burtea, Jan 13 2020
(Python)
from sympy import primerange
def aupto(lim): return [p for p in primerange(1, lim+1) if '0' in str(p)]
print(aupto(1910)) # Michael S. Branicky, Mar 11 2022

Crossrefs

Cf. A000040 (primes), A011540 (numbers that contain a 0).

Complement, in A000040, of zeroless primes A038618.

Cf. A164968 (Naughty primes: most digits are 0).

Sequence in context: A164739 A085821 A183087 * A243825 A345728 A309488

Adjacent sequences: A056706 A056707 A056708 * A056710 A056711 A056712

Keyword

nonn,base

Author

Robert G. Wilson v, Aug 10 2000

Status

approved