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%I #26 Dec 20 2022 18:39:26
%S 1,12,123456,123456789101112131415161718192021222324252627282930,
%T 12345678910111213141516171819202122232425262728293031323334353637383940414243444546474849505152535455565758596061626364656667686970717273747576777879808182838485868788
%N Numbers k such that (i) k is a concatenation of consecutive natural numbers starting at 1 and (ii) k+1 is prime.
%C 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]
%C 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
%e 12 is a term since it is the concatenation of 1 and 2, and 12+1 = 13 is prime.
%e 123456 is a concatenation, starting with 1, of consecutive natural numbers and 123456 + 1 = 123457 is prime.
%e k = 123456789101112131415161718192021222324252627282930 is a term since k+1 = 123456789101112131415161718192021222324252627282931 is prime.
%t Select[Table[FromDigits[Flatten[IntegerDigits/@Range[n]]],{n,100}],PrimeQ[#+1]&] (* _Harvey P. Dale_, Dec 20 2022 *)
%Y Cf. A007908, A359124, A359125.
%K base,nonn
%O 1,2
%A _Joseph L. Pe_, Apr 03 2002
%E Corrected by _Harvey P. Dale_, Dec 20 2022.
%E Edited by _N. J. A. Sloane_, Dec 20 2022
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