A121236 Primes of the form A001228(n) + 1 and A001228(n) - 1 where A001228 = orders of sporadic simple groups.

7919, 604801, 10200959, 44351999, 44352001, 50232961, 244823041, 460815505919, 64561751654399, 4089470473293004801, 4157776806543360001, 86775571046077562879

Offset: 1

Author

Jonathan Vos Post, Aug 21 2006

Keywords

• easy
• fini
• full
• nonn

Comments

This is not an arbitrary thing to do, as in some cases the sporadic group has an order depending on a specific power, as with A001228(1) + 1 = 7921 = 89^2 and A001228(3) + 1 = 175561 = 419^2. The largest integer to check is 1 + the order of the monster group, which is the semiprime 808017424794512875886459904961710757005754368000000001 = 18250906752127213 * 44272727693397225537389001926419074277.

Examples

			a(1) = 7919 = A001228(1) - 1.
a(2) = 604801 = A001228(5) + 1.
a(3) = 10200959 = A001228(6) - 1.
a(4) = 44351999 = A001228(7) - 1.
a(5) = 44352001 = A001228(7) + 1.
a(6) = 50232961 = A001228(8) + 1.
a(7) = 244823041 = A001228(9) + 1.
a(8) = 460815505919 = A001228(14) + 1.
a(9) = 64561751654399 = A001228(17) - 1.
a(10) = 4089470473293004801 = A001228(21) + 1.
a(11) = 4157776806543360001 = A001228(22) + 1.
a(12) = 86775571046077562879 = A001228(23) - 1.
		

Crossrefs

Cf. A000040, A001228.

Formula

({A001228(n) + 1} UNION {A001228(n) - 1}) INTERSECTION A000040.