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Numbers n such that the concatenation of the decimal numbers 1 through n, but omitting 2, is a prime.
2

%I #14 Nov 04 2018 18:21:57

%S 3,41,103,1713,2769

%N Numbers n such that the concatenation of the decimal numbers 1 through n, but omitting 2, is a prime.

%C The corresponding primes are the primes in A262572. Probabilistic arguments suggest the sequence is infinite.

%C a(6) > 10000, if it exists. - _Robert Price_, Nov 04 2018

%e The first two terms correspond to the primes 13 and 134567891011121314151617181920212223242526272829303132333435363738394041 (see A262298).

%e a(3) corresponds to a prime ending in 103, with 200 digits, a(4) to a probable prime ending in 1713, with 5744 digits, and a(5) to a probable prime ending in 2769, with 9968 digits. These three terms were found by _David Broadhurst_ on Oct 09 2015.

%Y Cf. A262572, A262298, A007908.

%K nonn,base,more

%O 1,1

%A _N. J. A. Sloane_, Oct 09 2015