A294132
Sorted list of prime factors of numbers of the form 3^(2^m) + 2^(2^m) with m >= 0.
Original entry on oeis.org
5, 13, 17, 97, 257, 401, 769, 1153, 3041, 14177, 65537, 286721, 1810433, 2752513, 4043777, 7340033, 13631489, 23068673, 72222721, 319291393, 348061697, 625483777, 3937533953, 54498164737, 106216554497, 121899667073, 151597350913, 342456532993
Offset: 1
The first 5 such numbers are 5, 13, 97, 6817, 43112257, 1853024483819137. Their prime factorizations are (5), (13), (97), (17) (401), (14177) (3041), (1153) (1607133116929). - _N. J. A. Sloane_, Oct 29 2017
- Arkadiusz Wesolowski, Table of n, a(n) for n = 1..48
- Anders Björn and Hans Riesel, Factors of generalized Fermat numbers, Math. Comp. 67 (1998), no. 221, pp. 441-446.
- Anders Björn and Hans Riesel, Table errata to “Factors of generalized Fermat numbers”, Math. Comp. 74 (2005), no. 252, p. 2099.
- Anders Björn and Hans Riesel, Table errata 2 to "Factors of generalized Fermat numbers", Math. Comp. 80 (2011), pp. 1865-1866.
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print1(5, ", "); forprime(p=13, 342456532993, z=znorder(Mod(3/2, p)); if(2^ispower(z)==z, print1(p, ", ")));
A294134
Sorted list of prime factors of numbers of the form 7^(2^m) + 2^(2^m) with m >= 0.
Original entry on oeis.org
3, 17, 53, 97, 257, 449, 2417, 7681, 8513, 65537, 89633, 114689, 339121, 876097, 1321729, 1454081, 2572289, 4638721, 5463041, 7340033, 27688961, 47047681, 62177153, 93847553, 113418241, 374734849, 3731619841, 13037142017, 13555990529, 13951408129, 142807662593
Offset: 1
- Arkadiusz Wesolowski, Table of n, a(n) for n = 1..43
- Anders Björn and Hans Riesel, Factors of generalized Fermat numbers, Math. Comp. 67 (1998), no. 221, pp. 441-446.
- Anders Björn and Hans Riesel, Table errata to “Factors of generalized Fermat numbers”, Math. Comp. 74 (2005), no. 252, p. 2099.
- Anders Björn and Hans Riesel, Table errata 2 to "Factors of generalized Fermat numbers", Math. Comp. 80 (2011), pp. 1865-1866.
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print1(3, ", "); forprime(p=17, 142807662593, z=znorder(Mod(7/2, p)); if(2^ispower(z)==z, print1(p, ", ")));
A294135
Sorted list of prime factors of numbers of the form 9^(2^m) + 2^(2^m) with m >= 0.
Original entry on oeis.org
5, 11, 17, 257, 449, 1601, 6577, 20353, 25601, 40961, 65537, 95873, 163841, 176129, 1179649, 8452097, 13631489, 26419201, 32310529, 38031361, 56867009, 59637761, 144310273, 480865793, 697434113, 1572864001, 2013265921, 7547650049, 62872289281, 483049603073
Offset: 1
- Arkadiusz Wesolowski, Table of n, a(n) for n = 1..43
- Anders Björn and Hans Riesel, Factors of generalized Fermat numbers, Math. Comp. 67 (1998), no. 221, pp. 441-446.
- Anders Björn and Hans Riesel, Table errata to “Factors of generalized Fermat numbers”, Math. Comp. 74 (2005), no. 252, p. 2099.
- Anders Björn and Hans Riesel, Table errata 2 to "Factors of generalized Fermat numbers", Math. Comp. 80 (2011), pp. 1865-1866.
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print1(5, ", "11, ", "); forprime(p=17, 483049603073, z=znorder(Mod(9/2, p)); if(2^ispower(z)==z, print1(p, ", ")));
A294136
Sorted list of prime factors of numbers of the form 11^(2^m) + 2^(2^m) with m >= 0.
Original entry on oeis.org
5, 13, 17, 241, 257, 12289, 14657, 26113, 52321, 65537, 98561, 235009, 697409, 23068673, 558205057, 755184641, 3433910273, 5557248001, 17343447041, 65886344833, 442483095553, 689863229441, 8142833614849, 10737426890753, 11598906596353, 57966757675009
Offset: 1
- Arkadiusz Wesolowski, Table of n, a(n) for n = 1..31
- Anders Björn and Hans Riesel, Factors of generalized Fermat numbers, Math. Comp. 67 (1998), no. 221, pp. 441-446.
- Anders Björn and Hans Riesel, Table errata to “Factors of generalized Fermat numbers”, Math. Comp. 74 (2005), no. 252, p. 2099.
- Anders Björn and Hans Riesel, Table errata 2 to "Factors of generalized Fermat numbers", Math. Comp. 80 (2011), pp. 1865-1866.
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print1(5, ", "13, ", "); forprime(p=17, 57966757675009, z=znorder(Mod(11/2, p)); if(2^ispower(z)==z, print1(p, ", ")));
Showing 1-4 of 4 results.
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