A342834 a(n) is the number whose decimal expansion consists of the concatenation of the largest 1-digit prime = 7, the largest 2-digit prime = 97, ... up to the largest n-digit prime = A003618(n).

7, 797, 797997, 7979979973, 797997997399991, 797997997399991999983, 7979979973999919999839999991, 797997997399991999983999999199999989, 797997997399991999983999999199999989999999937, 7979979973999919999839999991999999899999999379999999967

Offset: 1

Author

Bernard Schott, Mar 23 2021

Keywords

• nonn
• base

Comments

a(n) has n*(n+1)/2 digits.

a(1) = 7 and a(2) = 797, these are only 2 known indices for which a(n) = A338968(n).

The decimal expansion of the limit when n -> oo of a(n) is A340220.

Examples

			The greatest primes with 1, 2 and 3 digits are respectively 7, 97 and 997, hence, a(3) = 7||97||997 = 797997 where || stands for concatenation.
		

Crossrefs

Cf. A000217 (number of digits), A338968, A340220, A342835 (number of divisors), A342836 (smallest prime factor).

Programs

PARI

a(n) = my(s=""); for (k=1, n, s = Str(s, precprime(10^k))); eval(s); \\ Michel Marcus, Mar 24 2021

Python

from sympy import prevprime
def aupton(nn):
  astr, alst = "", []
  for n in range(1, nn+1):
    astr += str(prevprime(10**n)); alst.append(int(astr))
  return alst
print(aupton(10)) # Michael S. Branicky, Mar 23 2021