cp's OEIS Frontend

A088104 Smallest n-digit prime beginning with prime(n), or 0 if no such prime exists.

%I A088104 #25 Jun 18 2019 14:52:36
%S A088104 2,31,503,7001,11003,130003,1700021,19000013,230000003,2900000017,
%T A088104 31000000027,370000000003,4100000000003,43000000000063,
%U A088104 470000000000023,5300000000000129,59000000000000011,610000000000000031,6700000000000000021,71000000000000000047,730000000000000000001
%N A088104 Smallest n-digit prime beginning with prime(n), or 0 if no such prime exists.
%C A088104 Conjecture: No term is zero. Subsidiary sequences: (1) A088754 = number of n-digit primes beginning with prime(n). (2) A088755 = number of n-digit primes beginning with n.
%C A088104 If Legendre's conjecture is true, then no term is zero. - _Chai Wah Wu_, Jun 18 2019
%H A088104 David A. Corneth, <a href="/A088104/b088104.txt">Table of n, a(n) for n = 1..723</a>
%e A088104 a(6) = 130003 begins with prime(6) = 13 and has 6 digits.
%t A088104 Prepend[NextPrime[FromDigits[PadRight[IntegerDigits[#],PrimePi[#]]]]&/@Prime[Range[2,25]],2]  (* _Harvey P. Dale_, Jan 09 2011 *)
%o A088104 (PARI) a(n) = my(p=prime(n), d=digits(p)); c=nextprime(p*10^(n-#d)); cd=digits(c); if(vector(#d, i, cd[i]) == d, return(c), return(0)) \\ _David A. Corneth_, Apr 13 2019
%o A088104 (Python)
%o A088104 from sympy import prime, nextprime
%o A088104 def A088104(n):
%o A088104     p = prime(n)
%o A088104     return nextprime(p*10**(n-len(str(p)))-1) # _Chai Wah Wu_, Jun 18 2019
%Y A088104 Cf. A077504, A077505, A088105, A088754, A088755.
%K A088104 base,nonn
%O A088104 1,1
%A A088104 _Amarnath Murthy_, Sep 24 2003
%E A088104 More terms from _Ray Chandler_, Oct 15 2003
%E A088104 More terms from _David A. Corneth_, Apr 13 2019