A172315 Primes of the form 2^i*3^j - 1 with i + j = 13.

8191, 27647, 62207, 139967, 314927, 472391, 1062881

Offset: 1

Author

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Jan 31 2010

Keywords

• fini
• full
• nonn

Comments

Note that bases 2 = prime(1), 3 = prime(2)

13 = prime(2 x 3) = prime(prime(1) x prime(2))

Smallest term 8191 is the 5th Mersenne prime

It is a finite "FUN" sequence with 7 = prime(4) terms

Examples

			8191 = 2^13 - 1 = prime(1028)
27647 = 2^10 x 3^3 - 1 = prime(3016) = prime(2^3 x 13 x 29)
62207 = 2^8 x 3^5 - 1 = prime(6253) = prime(13^ 2 x 37)
139967 = 2^6 x 3^7 - 1 = prime(13005)
314927 = 2^4 x 3^9 - 1 = prime(27191), index is prime(2978)
472391 = 2^3 x 3^10 - 1 = prime(39419), index is prime(4150)
1062881 = 2 x 3^12 - 1 = prime(83024)
		

References

• Helmut Kracke, Mathe-musische Knobelisken, Duemmler Bonn, 2. Auflage 1983

Crossrefs

Cf. A005105, A168385, A168349

Programs

Mathematica

Select[Union[Flatten[{2^#[[1]] 3^#[[2]]-1,2^#[[2]] 3^#[[1]]-1}&/@ Table[ {n,13-n},{n,0,13}]]],PrimeQ] (* Harvey P. Dale, Jan 11 2016 *)