A294133
Sorted list of prime factors of numbers of the form 5^(2^m) + 2^(2^m) with m >= 0.
Original entry on oeis.org
7, 17, 29, 97, 193, 257, 641, 12289, 22993, 65537, 102593, 115201, 152833, 211457, 993793, 5189633, 26411009, 79280897, 93847553, 167772161, 230686721, 1364951041, 1573071713, 3221225473, 5488091137, 186678460417, 206158430209, 274568286337
Offset: 1
- Arkadiusz Wesolowski, Table of n, a(n) for n = 1..34
- 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(7, ", "); forprime(p=17, 274568286337, z=znorder(Mod(5/2, 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, ", ")));
A050244
Numbers k such that 2^k + 3^k is a semiprime.
Original entry on oeis.org
3, 6, 7, 8, 10, 11, 12, 14, 16, 22, 32, 34, 38, 82, 83, 106, 128, 149, 218, 223, 334, 412, 436, 599, 647, 916, 1373, 4414, 7246, 8423, 10118, 10942, 15898, 42422, 65986
Offset: 1
a(1)=3 because 2^3 + 3^3 = 5 * 7.
a(2)=6 because 2^6 + 3^6 = 13 * 61.
a(3)=7 because 2^7 + 3^7 = 5 * 463.
a(4)=8 because 2^8 + 3^8 = 17 * 401.
a(5)=10 because 2^10 + 3^10 = 13 * 4621.
a(6)=11 because 2^11 + 3^11 = 5 * 35839.
a(7)=12 because 2^12 + 3^12 = 97 * 5521.
a(8)=14 because 2^14 + 3^14 = 13 * 369181.
a(9)=16 because 2^16 + 3^16 = 3041 * 14177.
a(10)=22 because 2^22 + 3^22 = 13 * 2414250301.
a(11)=32 because 2^32 + 3^32 = 1153 * 1607133116929.
a(12)=34 because 2^34 + 3^34 = 13 * 1282861452271981.
a(13)=38 because 2^38 + 3^38 = 13 * 103911691734684541.
a(14)=82 because 2^82 + 3^82 = 13 * 102329189594547549657540565413396038701.
a(15)=83 because 2^83 + 3^83 = 5 * 798167678837469920188160718521149336927.
a(16)=106 because 2^106 + 3^106 = 13 * 28900785585664327723593061693364968422740414514061.
a(17)=128 because 2^128 + 3^128 = 257 * 45876204582640401445607833244277975113391731388650867226881.
a(18)=149 because 2^149 + 3^149 = 5 * 24665899002341798194980052306171212216360861465143461865961807325057879.
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Dec 30 2007
A094499
Smallest prime factor of 2^(2^n)+3^(2^n), i.e., exponents are powers of 2.
Original entry on oeis.org
13, 97, 17, 3041, 1153, 769, 257, 72222721, 4043777, 2330249132033, 625483777, 286721, 14496395542529, 2752513, 65537, 319291393, 54498164737
Offset: 1
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f[n_] := Block[{k = 1, m = 2^(n + 1)}, While[ Mod[ PowerMod[2, 2^n, k*m + 1] + PowerMod[3, 2^n, k*m + 1], k*m + 1] != 0, k++ ]; k*m + 1]; Table[ f[n], {n, 9}] (* Robert G. Wilson v, Jun 03 2004 *)
Showing 1-6 of 6 results.
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