A097525 Least k such that k*P(n)#-P(n+1) and k*P(n)#+P(n+1) are both primes with P(i)=i-th prime and P(i)#=i-th primorial.

4, 2, 1, 2, 14, 1, 4, 1, 5, 42, 3, 19, 33, 12, 48, 105, 26, 5, 35, 23, 49, 70, 160, 59, 52, 141, 105, 96, 154, 103, 174, 114, 140, 314, 615, 97, 42, 6, 781, 240, 8, 71, 764, 14, 321, 197, 916, 823, 901, 23, 390, 121, 1549, 646, 117, 622, 826, 671, 1577, 339, 313, 465, 62

Offset

1,1

Links

Table of n, a(n) for n=1..63.

Example

2*3*5*7-11=199 prime 2*3*5*7+11=221=13*17 composite
2*2*3*5*7-11=409 prime 2*2*3*5*7+11=431 prime
2*P(4)#-P(5) and 2*P(4)+P(5) both primes, so k=2 for n=4.

Mathematica

Primorial[n_] := Product[ Prime[i], {i, n}]; f[n_] := Block[{k = 1, p = Primorial[n], q = Prime[n + 1]}, While[k*p - q < 2 || !PrimeQ[k*p - q] || !PrimeQ[k*p + q], k++ ]; k]; Table[ f[n], {n, 63}] (* Robert G. Wilson v, Aug 31 2004 *)

Crossrefs

Sequence in context: A280988 A175665 A200586 * A309975 A010124 A271310

Adjacent sequences: A097522 A097523 A097524 * A097526 A097527 A097528

Keyword

easy,nonn

Author

Pierre CAMI, Aug 27 2004

Extensions

More terms from Robert G. Wilson v, Aug 31 2004

Status

approved