A357915 Concatenation of the decimal digits of {n, 1..n}.

11, 212, 3123, 41234, 512345, 6123456, 71234567, 812345678, 9123456789, 1012345678910, 111234567891011, 12123456789101112, 1312345678910111213, 141234567891011121314, 15123456789101112131415, 1612345678910111213141516

Offset: 1

Author

Mikk Heidemaa, Jan 18 2023

Keywords

• nonn
• base
• easy

Comments

Concatenation of the consecutive integers 1..n, with n prepended (n > 0).

The terms a(1), a(7), a(31), and a(337) are primes (of the form n1...n).

a(3643) is a 13469-digit probable prime (the number of digits is also a prime).

These indices 7, 31, 337, 3643 are themselves primes of the form 6m+1.

For the known terms a(n) which are primes and for a(3643), a(n) == 2 (mod 3).

There is no other prime term for n < 15000 (and no prime term with prime index n < 25000).

Examples

			a(2) = 212 since it is the concatenation of the consecutive positive integers <= 2, with 2 prepended.
		

Links

• Winston de Greef, Table of n, a(n) for n = 1..367
• G. L. Honaker, Jr. and Chris K. Caldwell, Prime Curios! 71234567

Crossrefs

Cf. A007908, A078257, A172495.

Programs

Mathematica

aUpTo[n_] := Table[ FromDigits @ Flatten @ IntegerDigits @ {i, Range @ i}, {i,n}]; aUpTo[999]

PARI

a(n) = my(s=Str(n)); for(k=1, n, s=Str(s, k)); eval(s); \\ Michel Marcus, Jan 20 2023

Python

def a(n): return int(str(n)+"".join(map(str, range(1, n+1))))
print([a(n) for n in range(1, 17)]) # Michael S. Branicky, Jan 20 2023

Formula

a(n) = concat(n, A007908(n)).