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A199340
Primes having only the (decimal) digits 0, 3 and 4.
14
3, 43, 433, 443, 3343, 3433, 4003, 30403, 33343, 33403, 34033, 34303, 34403, 40343, 40433, 43003, 43403, 300043, 300343, 304033, 304303, 304433, 330433, 333433, 334043, 334333, 334403, 343303, 343333, 343433, 400033, 403003, 403043, 403433, 430303, 430333
OFFSET
1,1
COMMENTS
All terms end in '3'. This could be used to speed up the given program.
A020461 is a subsequence. - Vincenzo Librandi, Jul 23 2015
MATHEMATICA
Select[Prime[Range[5 10^4]], Complement[IntegerDigits[#], {3, 4, 0}]=={} &] (* Vincenzo Librandi, Jul 23 2015 *)
Select[FromDigits/@Tuples[{0, 3, 4}, 6], PrimeQ] (* Harvey P. Dale, Mar 21 2020 *)
Select[10#+3&/@FromDigits/@Tuples[{0, 3, 4}, 5], PrimeQ] (* Harvey P. Dale, May 02 2022 *)
PROG
(PARI) a(n, list=0, L=[0, 3, 4], reqpal=0)={my(t); for(d=1, 1e9, u=vector(d, i, 10^(d-i))~; forvec(v=vector(d, i, [1+(i==1&!L[1]), #L]), isprime(t=vector(d, i, L[v[i]])*u)||next; reqpal && !isprime(A004086(t)) && next; list && print1(t", "); n--||return(t)))} \\ Syntax updated for current PARI version. - M. F. Hasler, Jul 25 2015
(Magma) [p: p in PrimesUpTo(5*10^5) | Set(Intseq(p)) subset [3, 4, 0]]; // Vincenzo Librandi, Jul 23 2015
(PARI) {forprime(p=3, 1e6, p%10==3&&!setminus(Set(digits(p)), [3, 4])&&print1(p", "))} \\ [0] evaluates to false. - M. F. Hasler, Jul 25 2015
CROSSREFS
Cf. Primes that contain only the digits (3,4,k): this sequence (k=0), A199341 (k=1), A199342 (k=2), A199345 (k=5), A199346 (k=6), A199347 (k=7), A199348 (k=8), A199349 (k=9).
Sequence in context: A199349 A197609 A199346 * A020461 A138974 A036940
KEYWORD
nonn,base
AUTHOR
M. F. Hasler, Nov 05 2011
STATUS
approved