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 A069675 Primes all of whose internal digits (if any) are 0. 21
 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 307, 401, 409, 503, 509, 601, 607, 701, 709, 809, 907, 1009, 2003, 3001, 4001, 4003, 4007, 5003, 5009, 6007, 7001, 8009, 9001, 9007, 10007, 10009 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Despite their initial density, these primes are rare. The value of a(310) = 9*10^2914 + 7. Beginning with a(54), this is a subsequence of A164968. Indeed, these could be called the "naughtiest" primes. - Harlan J. Brothers, Aug 17 2015 There are expected to be infinitely many terms, but growing very rapidly, something like a(n) ~ exp(exp(const * n)). - Robert Israel, Aug 17 2015 LINKS Charles R Greathouse IV, Table of n, a(n) for n = 1..263 Makoto Kamada, Prime numbers of the form k*10^n+1 Seth A. Troisi, Plot of log(log(a(n))) for 1 <= n <= 434 Seth A. Troisi, a(n) for n = 1 .. 434, a(n) in form "a * 10 ^ d + b" FORMULA a(n) >> 10^(n/24). - Charles R Greathouse IV, Sep 14 2015 EXAMPLE 4001 is in the sequence because it is prime and all the internal digits (the digits between 4 and 1) are zero. - Michael B. Porter, Aug 11 2016 MAPLE A := {}: for n to 1000 do p := ithprime(n): d := convert(p, base, 10): s := 0: for m from 2 to nops(d)-1 do s := s+d[m]: end do if s = 0 then A := `union`(A, {p}) end if: end do: A := A # César Eliud Lozada, Sep 04 2012 select(isprime, [\$1..9, seq(seq(seq(10^d*a+b, b=1..9), a=1..9), d=1..10)]); # Robert Israel, Aug 18 2015 MATHEMATICA Select[Prime[Range[1, 100000]], IntegerLength[#] < 3 || Union@Rest@Most@IntegerDigits[#, 10] == {0} &] (* Harlan J. Brothers, Aug 17 2015 *) Select[Join[Range[1, 99], Flatten[Table[a*10^d + b, {d, 2, 50}, {a, 1, 9}, {b, 1, 9}]]], PrimeQ[#] &] (* Seth A. Troisi, Aug 03 2016 *) PROG (PARI) go(n)=my(v=List(primes(4)), t); for(d=1, n-1, for(i=1, 9, forstep(j=1, 9, [2, 4, 2], if(isprime(t=10^d*i+j), listput(v, t))))); Vec(v) \\ Charles R Greathouse IV, Sep 14 2015 (Python) from sympy import isprime print([2, 3, 5, 7] + list(filter(isprime, (a*10**d+b for d in range(1, 101) for a in range(1, 10) for b in [1, 3, 7, 9])))) # Michael S. Branicky, May 08 2021 CROSSREFS Cf. A069676-A069684, A164968. Sequence in context: A163849 A124591 A164837 * A049585 A049549 A030291 Adjacent sequences: A069672 A069673 A069674 * A069676 A069677 A069678 KEYWORD nonn,base AUTHOR Amarnath Murthy, Apr 06 2002 EXTENSIONS Offset corrected and name changed by Arkadiusz Wesolowski, Sep 07 2011 STATUS approved

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Last modified April 18 18:58 EDT 2024. Contains 371781 sequences. (Running on oeis4.)