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

2,1

Links

Table of n, a(n) for n=2..59.

Formula

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

Example

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.

Mathematica

<<NumberTheory`NumberTheoryFunctions` sz[x_] :=FromDigits[Flatten[Table[IntegerDigits[Prime[j]], {j, 1, x}], 1]] Table[NextPrime[sz[w]]-PreviousPrime[sz[w]], {w, 1, 100}]

Prog

(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

Crossrefs

Cf. A019518, A074809, A104462, A104463.

Sequence in context: A369702 A033986 A049004 * A344103 A181107 A234974

Adjacent sequences: A104642 A104643 A104644 * A104646 A104647 A104648

Keyword

nonn,base

Author

Labos Elemer, Mar 18 2005

Extensions

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

Status

approved