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

2, 31, 503, 7001, 11003, 130003, 1700021, 19000013, 230000003, 2900000017, 31000000027, 370000000003, 4100000000003, 43000000000063, 470000000000023, 5300000000000129, 59000000000000011, 610000000000000031, 6700000000000000021, 71000000000000000047, 730000000000000000001

Offset

1,1

Comments

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.

If Legendre's conjecture is true, then no term is zero. - Chai Wah Wu, Jun 18 2019

Links

David A. Corneth, Table of n, a(n) for n = 1..723

Example

a(6) = 130003 begins with prime(6) = 13 and has 6 digits.

Mathematica

Prepend[NextPrime[FromDigits[PadRight[IntegerDigits[#], PrimePi[#]]]]&/@Prime[Range[2, 25]], 2]  (* Harvey P. Dale, Jan 09 2011 *)

Prog

(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
(Python)
from sympy import prime, nextprime
def A088104(n):
    p = prime(n)
    return nextprime(p*10**(n-len(str(p)))-1) # Chai Wah Wu, Jun 18 2019

Crossrefs

Cf. A077504, A077505, A088105, A088754, A088755.

Sequence in context: A218687 A071360 A108491 * A362860 A057692 A058244

Adjacent sequences: A088101 A088102 A088103 * A088105 A088106 A088107

Keyword

base,nonn

Author

Amarnath Murthy, Sep 24 2003

Extensions

More terms from Ray Chandler, Oct 15 2003

More terms from David A. Corneth, Apr 13 2019

Status

approved