A104645 Difference between the previous and the next primes to x, where x is the number obtained from concatenation of the first n primes (A019518).

10, 6, 20, 24, 24, 60, 18, 48, 100, 48, 156, 74, 88, 68, 42, 126, 366, 106, 186, 136, 228, 104, 30, 246, 52, 218, 814, 58, 536, 174, 90, 924, 180, 298, 120, 330, 96, 508, 504, 60, 762, 588, 330, 138, 552, 726, 452, 634, 660, 354, 534, 1770, 52, 262, 834, 790, 250, 624

Offset: 2

Author

Labos Elemer, Mar 18 2005

Keywords

• nonn
• base

Examples

			For n=4, concatenate(2,3,5,7) gives 2357. The closest other primes are 2371 and 2351 and their difference is a(4)=20.
		

Crossrefs

Cf. A019518, A074809, A104462, A104463.

Programs

Mathematica

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PARI

A019518(n)=my(k="");forprime(p=2,prime(n),k=Str(k,p));eval(k)
a(n)=my(k=A019518(n));nextprime(k+1)-precprime(k-1) \\ Charles R Greathouse IV, Apr 28 2010

Formula

a(n) = A151800(A019518(n)) - A151799(A019518(n)).

Extensions

Corrected, extended, and edited by Charles R Greathouse IV, Apr 28 2010