A005542 Numbers k such that 10*3^k - 1 is prime. (Formerly M0589)

1, 2, 3, 4, 8, 10, 14, 20, 22, 26, 30, 38, 39, 49, 54, 58, 70, 81, 84, 87, 102, 111, 140, 159, 207, 224, 328, 358, 360, 447, 484, 908, 1083, 1242, 1461, 1705, 4624, 5199, 7106, 8667, 11157, 13130, 28052, 30483, 32166, 34447, 36986, 86578, 89940, 120433, 140743, 147308, 159276, 165543

Offset

1,2

Comments

a(56) > 2*10^5. - Robert Price, Mar 16 2014

All terms are verified primes (i.e., not probable primes). - Robert Price, Mar 16 2014

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=1..54.

H. C. Williams and C. R. Zarnke, Some prime numbers of the forms 2*3^n+1 and 2*3^n-1, Math. Comp., 26 (1972), 995-998.

Mathematica

Do[ If[ PrimeQ[ 10*3^n - 1], Print[n] ], {n, 1, 12901} ]

Prog

(PARI) v=[ ]; for(n=1, 1900, if(isprime(10*3^n-1), v=concat(v, n), )); v

Crossrefs

Sequence in context: A302406 A328092 A242762 * A037171 A308811 A295296

Adjacent sequences: A005539 A005540 A005541 * A005543 A005544 A005545

Keyword

hard,nonn

Author

N. J. A. Sloane

Extensions

More terms from Robert G. Wilson v, Feb 05 2001

a(42)-a(55) from Robert Price, Mar 16 2014

Status

approved