A210461 Cipolla pseudoprimes to base 3: (9^p-1)/8 for any odd prime p.

91, 7381, 597871, 3922632451, 317733228541, 2084647712458321, 168856464709124011, 1107867264956562636991, 588766087155780604365200461, 47690053059618228953581237351, 25344449488056571213320166359119221, 166284933091139163730593611482181209801

Offset

1,1

Comments

This is the case a=3 of Theorem 1 in the paper of Hamahata and Kokubun (see Links section).

References

Michele Cipolla, Sui numeri composti P che verificano la congruenza di Fermat a^(P-1) = 1 (mod P), Annali di Matematica 9 (1904), p. 139-160.

Links

Bruno Berselli, Table of n, a(n) for n = 1..50

Umberto Cerruti, Pseudoprimi di Fermat e numeri di Carmichael (in Italian), 2013.

Y. Hamahata and Y. Kokubun, Cipolla Pseudoprimes, Journal of Integer Sequences, Vol. 10 (2007).

Example

91 is in the sequence because 91=((3^3-1)/2)*((3^3+1)/4), even if p=3 divides 3*(3^2-1), and 3^90 = (91*8+1)^15 == 1 (mod 91).
7381 is in the sequence because 7381=((3^5-1)/2)*((3^5+1)/4) and 3^7380 = (7381*472400+1)^369 == 1 (mod 7381).

Maple

P:=proc(q)local n;
for n from 2 to q do print((9^ithprime(n)-1)/8);
od; end: P(100); # Paolo P. Lava, Oct 11 2013

Mathematica

(9^# - 1)/8 & /@ Prime[Range[2, 12]]

Prog

(Magma) [(9^NthPrime(n)-1)/8: n in [2..12]];
(Maxima)
Prime(n) := block(if n = 1 then return(2), return(next_prime(Prime(n-1))))$
makelist((9^Prime(n)-1)/8, n, 2, 12);
(Haskell)
a210461 = (`div` 8) . (subtract 1) . (9 ^) . a065091
-- Reinhard Zumkeller, Jan 22 2013

Crossrefs

Cf. A005935, A002452, A065091, A210454, A217853.

Sequence in context: A103855 A238541 A217853 * A022253 A172174 A060078

Adjacent sequences: A210458 A210459 A210460 * A210462 A210463 A210464

Keyword

nonn

Author

Bruno Berselli, Jan 22 2013 - proposed by Umberto Cerruti (Department of Mathematics "Giuseppe Peano", University of Turin, Italy)

Status

approved