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Primes in the concatenation of consecutive numbers beginning with 2.
6

%I #43 Nov 05 2018 21:07:49

%S 2,23,23456789,23456789101112131415161718192021222324252627

%N Primes in the concatenation of consecutive numbers beginning with 2.

%C Sum of reciprocals = 0.5434783035011462065880780409...

%C 23, 4567 and 89 are prime numbers, thus a(3) = A262571(9) = 23456789 is a prime obtained by concatenating 3 primes that are themselves the concatenation of consecutive integers. - _XU Pingya_, Apr 16 2017

%C No other primes less than the concatenation of 2,3,4,5,6,7,8,9,10,11,12,...,9999. - _Robert Price_, Nov 04 2018

%t Select[Table[FromDigits[Flatten[IntegerDigits[Range[2, n]]]], {n, 2, 30}], PrimeQ[#] & ] (* _Robert Price_, Nov 05 2018 *)

%o (PARI) concatprime(n,p) = { sr=0; y=""; for(x=p,n, y=concat(Str(y),Str(x)); z=eval(y); if(ispseudoprime(z),print1(z","); sr+=1./z; ); ); print(); print(sr) }

%Y Primes in A262571.

%Y See A262300 for more information.

%Y See also A007908 for the numbers 1234...n.

%K nonn,base,more

%O 1,1

%A _Cino Hilliard_, Jan 14 2004

%E Offset corrected by _Michel Marcus_, Apr 21 2017