A049462 a(n) is the smallest n-digit prime p such that the concatenation a(1)a(2)...a(n-1)p is prime, with a(1) = 2.

2, 11, 151, 1013, 10867, 100673, 1000357, 10000931, 100000213, 1000000901, 10000001797, 100000000283, 1000000001911, 10000000012553, 100000000006087, 1000000000011317, 10000000000003471, 100000000000017431

Offset

1,1

Comments

The corresponding primes are certified for 44 < n < 60 (for the first 15 titanic primes). - Metin Sariyar, Oct 23 2020

Links

Metin Sariyar, Table of n, a(n) for n = 1..100

Example

Starting with an initial prime of 2, next the smallest 2-digit prime which gives a prime is 11 (211, a prime), then 151 (3-digit prime) is the smallest to make 211151 a prime, etc.

Mathematica

NextPrim[n_] := Block[{k = n + 1}, While[ ! PrimeQ[k], k++ ]; k]; a[1] = 2; a[n_] := a[n] = Block[{p = Sum[ a[i]*10^(n(n + 1)/2 - i(i + 1)/2), {i, 1, n - 1}], q = NextPrim[10^(n - 1)]}, While[ !PrimeQ[p + q], q = NextPrim[q]]; q]; Table[ a[n], {n, 1, 19}] (* Robert G. Wilson v, Oct 18 2003 *)

Crossrefs

Cf. A080155, A083758.

Sequence in context: A111014 A171184 A297676 * A227328 A287149 A188684

Adjacent sequences: A049459 A049460 A049461 * A049463 A049464 A049465

Keyword

nonn,base

Author

Jeff Heleen, Oct 13 2003

Extensions

More terms from Robert G. Wilson v, Oct 18 2003

Status

approved