A069048 Numbers k such that (i) k is a concatenation of consecutive natural numbers starting at 1 and (ii) k+1 is prime.

1, 12, 123456, 123456789101112131415161718192021222324252627282930, 12345678910111213141516171819202122232425262728293031323334353637383940414243444546474849505152535455565758596061626364656667686970717273747576777879808182838485868788

Offset: 1

Author

Joseph L. Pe, Apr 03 2002

Keywords

• base
• nonn

Comments

Let n be a concatenation of consecutive natural numbers, starting from 1. Is n ever a prime number? [See A007908 for much more about this question. - N. J. A. Sloane, Dec 20 2022]

a(5) has 167 digits. There are no further terms 123...n for n <= 1000 (123...1000 has 2893 digits). - Harvey P. Dale, Dec 20 2022

Examples

			12 is a term since it is the concatenation of 1 and 2, and 12+1 = 13 is prime.
123456 is a concatenation, starting with 1, of consecutive natural numbers and 123456 + 1 = 123457 is prime.
k = 123456789101112131415161718192021222324252627282930 is a term since k+1 = 123456789101112131415161718192021222324252627282931 is prime.
		

Crossrefs

Cf. A007908, A359124, A359125.

Programs

Mathematica

Select[Table[FromDigits[Flatten[IntegerDigits/@Range[n]]],{n,100}],PrimeQ[#+1]&] (* Harvey P. Dale, Dec 20 2022 *)

Extensions

Corrected by Harvey P. Dale, Dec 20 2022.

Edited by N. J. A. Sloane, Dec 20 2022