A159611
Indices of the Fermat primes in the sequence of primes.
Original entry on oeis.org
2, 3, 7, 55, 6543
Offset: 1
3, the 1st Fermat prime is the 2nd prime, so a(1) = 2.
17, the 3rd Fermat prime is the 7th prime, so a(3) = 7.
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import Data.List (elemIndices)
a159611 n = a159611_list !! (n-1)
a159611_list = map (+ 2) $ elemIndices 0 a098006_list
-- Reinhard Zumkeller, Mar 26 2013
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PrimePi/@{3,5,17,257,65537} (* Harvey P. Dale, Aug 07 2022 *)
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for(i=0, 10, isprime(f=2^2^i+1) & print1(primepi(f), ", ")) \\ Michel Marcus, Apr 28 2016
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a152155(n) = centerlift(Mod(3, 2^(2^n)+1)^(2^(2^n-1)))
print1(2, ", "); for(x=0, oo, if(a152155(x)==-1, print1(primepi(2^(2^x)+1), ", "))) \\ Felix Fröhlich, Apr 30 2021
A152153
Positive residues of Pepin's Test for Fermat numbers using the base 3.
Original entry on oeis.org
0, 4, 16, 256, 65536, 10324303, 11860219800640380469, 110780954395540516579111562860048860420, 5864545399742183862578018016183410025465491904722516203269973267547486512819
Offset: 0
Dennis Martin (dennis.martin(AT)dptechnology.com), Nov 27 2008
a(4) = 3^(32768) (mod 65537) = 65536 = -1 (mod F(4)), therefore F(4) is prime.
a(5) = 3^(2147483648) (mod 4294967297) = 10324303 (mod F(5)), therefore F(5) is composite.
- M. Krizek, F. Luca & L. Somer, 17 Lectures on Fermat Numbers, Springer-Verlag NY 2001, pp. 42-43.
A152154
Positive residues of Pepin's Test for Fermat numbers using either 5 or 10 for the base.
Original entry on oeis.org
2, 0, 16, 256, 65536, 3484838166, 17225898269543404863, 6964187975677595099156927503004398881, 14553806122642016769237504145596730952769427034161327480375008633175279343120
Offset: 0
Dennis Martin (dennis.martin(AT)dptechnology.com), Nov 27 2008
a(4) = 5^(32768) (mod 65537) = 65536 = -1 (mod F(4)), therefore F(4) is prime.
a(5) = 5^(2147483648) (mod 4294967297) = 3484838166 (mod F(5)), therefore F(5) is composite.
- M. Krizek, F. Luca & L. Somer, 17 Lectures on Fermat Numbers, Springer-Verlag NY 2001, pp. 42-43.
A152156
Minimal residues of Pepin's Test for Fermat Numbers using either 5 or 10 for the base.
Original entry on oeis.org
-1, 0, -1, -1, -1, -810129131, -1220845804166146754, 6964187975677595099156927503004398881, 14553806122642016769237504145596730952769427034161327480375008633175279343120
Offset: 0
Dennis Martin (dennis.martin(AT)dptechnology.com), Nov 27 2008
a(4) = 5^(32768) (mod 65537) = 65536 = -1 (mod F(4)), therefore F(4) is prime.
a(5) = 5^(2147483648) (mod 4294967297) = -810129131 (mod F(5)), therefore F(5) is composite.
- M. Krizek, F. Luca & L. Somer, 17 Lectures on Fermat Numbers, Springer-Verlag NY 2001, pp. 42-43.
A281576
Composite Fermat numbers.
Original entry on oeis.org
4294967297, 18446744073709551617, 340282366920938463463374607431768211457, 115792089237316195423570985008687907853269984665640564039457584007913129639937
Offset: 1
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a152155(n) = centerlift(Mod(3, 2^(2^n)+1)^(2^(2^n-1)))
terms(n) = my(i=0, k=1); while(1, if(a152155(k)!=-1, print1(2^(2^k)+1, ", "); i++); if(i==n, break); k++)
terms(4) \\ print initial 4 terms
A281577
Irregular triangle read by rows: T(n, k) = A281576(n) modulo p^2, where p is the k-th prime factor of A281576(n) with p < sqrt(A281576(n)).
Original entry on oeis.org
28204, 17161560961, 2451293172821355028751076998879853, 1409441895293467096954080352837, 1385195550582, 17782786311867894562037823351528977990025091057921642664123352687840735480821116989430796689072791
Offset: 1
Triangle T(n, k) starts
28204
17161560961
2451293172821355028751076998879853
1409441895293467096954080352837
1385195550582, T(5, 2)
Note: T(5, 2) is not displayed here due to its size. The term can be seen in the Data section.
- P. Ribenboim, The Little Book of Bigger Primes, Springer Verlag, 1991.
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a152155(n) = centerlift(Mod(3, 2^(2^n)+1)^(2^(2^n-1)))
row(n) = my(i=0, k=1); while(1, if(a152155(k)!=-1, i++); if(i==n, forprime(p=1, sqrtint(2^(2^k)+1), if(Mod(2, p)^(2^k)==-1, print1(lift(Mod(2, p^2)^(2^k))+1, ", ")))); k++)
trianglerows(n) = for(k=1, n, row(k); print(""))
Showing 1-6 of 6 results.
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