A262250 Primes having exactly one digit in {1, 3, 7, 9}.

3, 7, 23, 29, 41, 43, 47, 53, 59, 61, 67, 83, 89, 223, 227, 229, 241, 251, 257, 263, 269, 281, 283, 401, 409, 421, 443, 449, 457, 461, 463, 467, 487, 503, 509, 521, 523, 541, 547, 557, 563, 569, 587, 601, 607, 641, 643, 647, 653, 659, 661, 683, 809, 821, 823, 827, 829, 853, 857, 859, 863, 881, 883, 887, 2003, 2027, 2029, 2053

Offset: 1

Author

Vladimir Shevelev, Sep 21 2015

Keywords

• nonn
• base

Comments

How can one prove that the sequence is infinite?

Probabilistic arguments imply that the number of terms not exceeding x is not less than 5/9*log(10)/log(6)*x^(log(6)/log(10))/log(x) = 0.7139...*x^0.778.../log(x).

Links

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

Crossrefs

Cf. A000040, A029743.

Programs

Mathematica

Select[Prime@ Range@ 310, Total@ Drop[First /@ Partition[DigitCount@ #, 2, 2], {3}] == 1 &] (* Michael De Vlieger, Sep 21 2015 *)

PARI

nbd(vd, d) = #select(i->(i == d), vd);
lista(nn) = {forprime(p=2, nn, vd = digits(p); if (nbd(vd,1) + nbd(vd,3) + nbd(vd,7) + nbd(vd,9) == 1, print1(p, ", ")););} \\ Michel Marcus, Sep 22 2015

PARI

list(lim)=my(v=List([3])); forprime(p=7,lim, if(#setintersect(Set(digits(p\10)), [1,3,7,9])==0, listput(v,p))); Vec(v) \\ Charles R Greathouse IV, Sep 22 2015

Perl

use ntheory ":all"; say join ", ", grep { tr/1379// == 1 } @{primes(3000)}; # Dana Jacobsen, Oct 13 2015