A210454 Cipolla pseudoprimes to base 2: (4^p-1)/3 for any prime p greater than 3.

341, 5461, 1398101, 22369621, 5726623061, 91625968981, 23456248059221, 96076792050570581, 1537228672809129301, 6296488643826193618261, 1611901092819505566274901, 25790417485112089060398421, 6602346876188694799461995861

Offset: 1

Author

Bruno Berselli, Jan 21 2013 - proposed by Umberto Cerruti (Department of Mathematics "Giuseppe Peano", University of Turin, Italy)

Keywords

• nonn

Comments

This is the case a=2 of Theorem 1 in the paper of Hamahata and Kokubun (see Links section).

Named after the Italian mathematician Michele Cipolla (1880-1947). - Amiram Eldar, Jun 15 2021

Links

• Bruno Berselli, Table of n, a(n) for n = 1..50
• Umberto Cerruti, Pseudoprimi di Fermat e numeri di Carmichael (in Italian), 2013. The sequence is on page 3.
• Michele Cipolla, Sui numeri composti P, che verificano la congruenza di Fermat a^(P-1) = 1 (mod P), Annali di Matematica, Vol. 9 (1904), pp. 139-160.
• Y. Hamahata and Y. Kokubun, Cipolla Pseudoprimes, Journal of Integer Sequences, Vol. 10 (2007), Article 07.8.6.

Crossrefs

Cf. A001567, A002450, A210461, A215848, A216170.

Programs

Haskell

a210454 = (`div` 3) . (subtract 1) . (4 ^) . a000040 . (+ 2)
-- Reinhard Zumkeller, Jan 22 2013

Magma

[(4^NthPrime(n)-1)/3: n in [3..15]];

Maple

P:=proc(q)local n;
for n from 3 to q do print((4^ithprime(n)-1)/3);
od; end: P(100); # Paolo P. Lava, Oct 11 2013

Mathematica

(4^# - 1)/3 & /@ Prime[Range[3, 15]]

Maxima

Prime(n) := block(if n = 1 then return(2), return(next_prime(Prime(n-1))))$
makelist((4^Prime(n)-1)/3, n, 3, 15);

PARI

a(n)=4^prime(n+2)\3 \\ Charles R Greathouse IV, Jul 09 2015