A089987 Primes in the concatenation of consecutive numbers beginning with 2.

2, 23, 23456789, 23456789101112131415161718192021222324252627

Offset: 1

Author

Cino Hilliard, Jan 14 2004

Keywords

• nonn
• base
• more

Comments

Sum of reciprocals = 0.5434783035011462065880780409...

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

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

Crossrefs

Primes in A262571.

See A262300 for more information.

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

Programs

Mathematica

Select[Table[FromDigits[Flatten[IntegerDigits[Range[2, n]]]], {n, 2, 30}], PrimeQ[#] & ] (* Robert Price, Nov 05 2018 *)

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) }

Extensions

Offset corrected by Michel Marcus, Apr 21 2017