A342835 -id:A342835 - cp's OEIS frontend

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

Bernard Schott, Mar 23 2021

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.

			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.

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

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

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

A342836 a(n) is the smallest prime factor of A342834(n).

Original entry on oeis.org

7, 797, 3, 7, 37, 3023681, 43, 1249, 7, 3, 23, 11, 3, 19, 3, 13390093693131976661567, 193, 2069, 11, 41, 3, 71, 3, 996370591, 3, 101, 1123, 54367, 159469, 151, 29, 3, 7

Offset: 1

Bernard Schott, Mar 24 2021

a(n) = A342834(n) for n = 1 and n = 2, no other solution is known.
No primes through a(258). - Michael S. Branicky, Mar 25 2021
a(34) <= 7944676315964871787139677901. a(35)..a(40) = 2089, 11, 3, 23, 3, 11. a(42)=3. - Chai Wah Wu, Mar 26 2021

			As A342834(5) = 7||97||997||9973||99991 = 797997997399991 = 37 * 951649 * 22663307, then a(5) = 37.

Chai Wah Wu, terms a(44)..a(84)

Cf. A020639, A338968, A342834, A342835.

a(n) = A020639(A342834(n)).

a(4)-a(14) from Daniel Suteu, Mar 24 2021

a(15)-a(33) from Michael S. Branicky and Apurva Rai, Mar 25 2021

A342838 Indices m such that A342834(m) is not squarefree.

Original entry on oeis.org

21, 31, 32, 39, 42, 62, 67, 75, 82, 91, 93, 97, 104, 109, 121, 127, 135, 137, 139, 140, 145, 146

Offset: 1

Bernard Schott and Daniel Suteu, Apr 01 2021

From the factorization of the initial terms of A342834, it may appear that A342834(n) is always squarefree, but this is false, and that present sequence lists the exceptions.

Cf. A013929, A342834, A342835, A342836, A342837.

f(n) = my(s=""); for (k=1, n, s = Str(s, precprime(10^k))); eval(s); \\ A342834
isok(m) = !issquarefree(f(m)); \\ Michel Marcus, Apr 01 2021

cp's OEIS Frontend

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).

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A342836 a(n) is the smallest prime factor of A342834(n).

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A342838 Indices m such that A342834(m) is not squarefree.

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