A074365 Smallest prime > the concatenation of the first n natural numbers.

2, 13, 127, 1237, 12347, 123457, 1234577, 12345701, 123456791, 12345678923, 1234567891013, 123456789101119, 12345678910111223, 1234567891011121343, 123456789101112131449, 12345678910111213141523, 1234567891011121314151753, 123456789101112131415161869

Offset

1,1

Links

Michael S. Branicky, Table of n, a(n) for n = 1..369 (all terms with <= 1000 digits).

Formula

a(n) = nextprime(A007908(n)). - Sean A. Irvine, Jan 20 2025

Example

The first prime > 123, the concatenation of the first three natural numbers, is 127. Hence a(3) = 127.

Maple

a:= n-> nextprime(parse(cat($1..n))):
seq(a(n), n=1..19);  # Alois P. Heinz, Feb 13 2021

Mathematica

p[n_] := Module[{r, i}, r = 2; i = 1; While[r <= n, i = i + 1; r = Prime[i]]; r]; s = ""; a = {}; Do[s = s <> ToString[Prime[i]]; a = Append[a, p[ToExpression[s]]], {i, 1, 8}]; a
Table[NextPrime[FromDigits[Flatten[IntegerDigits/@Range[n]]]], {n, 20}] (* Harvey P. Dale, Jan 16 2018 *)

Prog

(Python)
from sympy import nextprime
def a(n):
  return nextprime(int("".join(map(str, (i for i in range(1, n+1)))))-1)
print([a(n) for n in range(1, 19)]) # Michael S. Branicky, Feb 13 2021

Crossrefs

Cf. A007908.

Sequence in context: A372103 A394722 A073559 * A071362 A108471 A036078

Adjacent sequences: A074362 A074363 A074364 * A074366 A074367 A074368

Keyword

base,nonn

Author

Joseph L. Pe, Sep 26 2002

Extensions

More terms from Lior Manor, Oct 08 2002

a(18) and beyond from Michael S. Branicky, Feb 13 2021

Status

approved