A227856 Sequence of pairs k,g with k<3*2^n the smallest such that 3*2^n+k, 3*2^n+k+g, 3*2^n+k+2*g are three consecutive primes in arithmetic progression starting at n=5 as there is not any solution for n<5.

55, 6, 7, 12, 173, 6, 173, 6, 205, 6, 229, 6, 113, 6, 203, 6, 95, 6, 475, 6, 163, 6, 119, 12, 377, 18, 1045, 6, 133, 12, 551, 24, 131, 12, 259, 6, 1105, 42, 539, 6, 1487, 18, 1295, 12, 5, 12, 289, 36, 311, 36, 269, 6, 2833, 6, 1813, 18, 835, 6, 319, 6, 587, 6, 239, 30, 1225, 6, 1825, 12, 973, 12, 89, 30, 551, 12, 1805, 30, 1039, 18, 1219, 6

Offset: 5

Author

Pierre CAMI, Nov 01 2013

Keywords

• nonn

Comments

The ratio k/n^2 is in average near 0.8 and < 7 for n<701.

The ratio g/n^2 is in average near 0.5 and < 4 for n<701.

If 3*2^n+k > 10^22 the numbers are probable primes.

Examples

			3*2^5+55=151, 3*2^5+55+6=157 3*2^5+55*2*6=163
151, 157, 163 three consecutive primes in arithmetic progression 6, so first pair is 55, 6
		

Links

• Pierre CAMI, Table of n, a(n) for n = 5..1396

Crossrefs

Cf. A230699, A230852