A124155 19^p - 18^p, where p = Prime[n].

37, 1027, 586531, 281651707, 52221848818987, 21230018596585891, 3294475298046105653971, 1270184310304975912766347, 183481914331285799334907290427, 9601090905261258491400850200348915811

Offset: 1

Author

Alexander Adamchuk, Dec 01 2006

Keywords

• nonn

Comments

The first prime in a(n) is a(1) = 37 = 19^2 - 18^2. The second prime in a(n) is a(1331) = 19^10957 - 18^10957. It has 14012 decimal digits. Note that 1331 = 11^3, Prime[11^3] = 10957. Last digit of a(n) is 1 or 7. It appears that 3^2 divides a(n) - 1. Also it appears that 7^3 divides all a(n) - 1 for n>2. a(n) - 1 is divisible by 7^m, where m(n) = {0,0,3,7,3,6,3,6,3,3,6,6,3,...}. 7^6 divides a(n) - 1 for n = {4,6,8,11,12,14,18,19,21,22,25,27,29,31,34,36,37,38,42,44,46,47,48,50,53,58,59,61,63,65,67,68,70,73,74,75,78,80,82,84,85,88,90,93,95,99,100,...}. 7^7 divides a(n) - 1 for n = {4,14,31,47,68,75,82,90,101,115,122,134,153,163,169,177,183,213,226,233,251,269,295,...}. 7^8 divides a(n) - 1 for n = {153,233,383,493,531,669,775,839,871,907,937,...}.

Crossrefs

Cf. A121091 = Smallest nexus prime of the form n^p - (n-1)^p, where p is odd prime. Cf. A125713 = Smallest odd prime p such that (n+1)^p - n^p is prime.

Programs

Mathematica

Table[19^Prime[n]-18^Prime[n],{n,1,15}]

Formula

a(n) = 19^Prime[n] - 18^Prime[n].