A005266 -id:A005266 - OEIS

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A000058

Sylvester's sequence: a(n+1) = a(n)^2 - a(n) + 1, with a(0) = 2.
(Formerly M0865 N0331)

+10
108

2, 3, 7, 43, 1807, 3263443, 10650056950807, 113423713055421844361000443, 12864938683278671740537145998360961546653259485195807

(list; graph; refs; listen; history; text; internal format)

A000945

Euclid-Mullin sequence: a(1) = 2, a(n+1) is smallest prime factor of 1 + Product_{k=1..n} a(k).
(Formerly M0863 N0329)

+10
101

2, 3, 7, 43, 13, 53, 5, 6221671, 38709183810571, 139, 2801, 11, 17, 5471, 52662739, 23003, 30693651606209, 37, 1741, 1313797957, 887, 71, 7127, 109, 23, 97, 159227, 643679794963466223081509857, 103, 1079990819, 9539, 3143065813, 29, 3847, 89, 19, 577, 223, 139703, 457, 9649, 61, 4357

(list; graph; refs; listen; history; text; internal format)

A000946

Euclid-Mullin sequence: a(1) = 2, a(n+1) is the largest prime factor of 1 + Product_{k=1..n} a(k).
(Formerly M0864 N0330)

+10
53

2, 3, 7, 43, 139, 50207, 340999, 2365347734339, 4680225641471129, 1368845206580129, 889340324577880670089824574922371, 20766142440959799312827873190033784610984957267051218394040721

(list; graph; refs; listen; history; text; internal format)

A005265

a(1)=3, b(n) = Product_{k=1..n} a(k), a(n+1) is the smallest prime factor of b(n)-1.
(Formerly M2246)

+10
47

3, 2, 5, 29, 11, 7, 13, 37, 32222189, 131, 136013303998782209, 31, 197, 19, 157, 17, 8609, 1831129, 35977, 508326079288931, 487, 10253, 1390043, 18122659735201507243, 25319167, 9512386441, 85577, 1031, 3650460767, 107, 41, 811, 15787, 89, 68168743, 4583, 239, 1283, 443, 902404933, 64775657, 2753, 23, 149287, 149749, 7895159, 79, 43, 1409, 184274081, 47, 569, 63843643

(list; graph; refs; listen; history; text; internal format)

A051308

Euclid-Mullin sequence (A000945) with initial value a(1)=5 instead of a(1)=2.

+10
39

5, 2, 11, 3, 331, 19, 199, 53, 21888927391, 29833, 101, 71, 23, 311, 7, 72353, 13, 227, 96014559769, 5641, 41, 82107739003, 67, 169637539, 61, 29, 31319, 17, 97, 238591921, 313, 102065429, 157, 37, 595553520313, 244217, 241, 4773229353714971081083834237, 103

(list; graph; refs; listen; history; text; internal format)

A051335

Euclid-Mullin sequence (A000945) with initial value a(1)=127 instead of a(1)=2.

+10
33

127, 2, 3, 7, 5, 149, 19, 41, 23899, 139, 43, 761, 281, 17, 53, 2551, 23, 20149, 100720363856036298033578901613089271, 31, 179, 11, 13, 523, 282995646721, 2871347, 83, 10744429, 1031, 427773048135533, 97, 78506876242349, 67

(list; graph; refs; listen; history; text; internal format)

A057204

Primes congruent to 1 mod 6 generated recursively. Initial prime is 7. The next term is p(n) = Min_{p is prime; p divides 4Q^2+3; p mod 6 = 1}, where Q is the product of previous entries of the sequence.

+10
28

7, 199, 7761799, 487, 67, 103, 3562539697, 7251847, 13, 127, 5115369871402405003, 31, 697830431171707, 151, 3061, 229, 193, 5393552285540920774057256555028583857599359699, 709, 397, 37, 61, 46168741, 3127279, 181, 122268541

(list; graph; refs; listen; history; text; internal format)

A057208

Primes of the form 8k+5 generated recursively: a(1)=5, a(n) = least prime p == 5 (mod 8) with p | 4+Q^2, where Q is the product of all previous terms in the sequence.

+10
25

5, 29, 1237, 32171803229, 829, 405565189, 14717, 39405395843265000967254638989319923697097319108505264560061, 282860648026692294583447078797184988636062145943222437, 53, 421, 13, 109, 4133, 6476791289161646286812333, 461, 34549, 453690033695798389561735541

(list; graph; refs; listen; history; text; internal format)

A051334

Euclid-Mullin sequence (A000945) with initial value a(1)=8191 instead of a(1)=2.

+10
12

8191, 2, 3, 7, 53, 1399, 5, 19, 646843, 26945441, 109, 443, 90670999, 280460690293140589, 907, 16293787, 3655513, 499483, 131, 21067, 143797, 54540542259000816707816058313971443, 392963, 977, 11, 5021, 179, 439, 353, 34417238589462247, 1193114397863177, 13, 59, 31643, 79399, 73, 43, 16639867

(list; graph; refs; listen; history; text; internal format)

A051309

Euclid-Mullin sequence (A000945) with initial value a(1)=11 instead of a(1)=2.

+10
5

11, 2, 23, 3, 7, 10627, 433, 17, 13, 10805892983887, 73, 6397, 19, 489407, 2753, 87491, 18618443, 5, 31, 113, 41, 10723, 35101153, 25243, 374399, 966011, 293821591198219762366057, 234947, 4729, 27953, 3256171, 331, 613, 67, 272646324430637, 34281113, 21050393332691947013, 61, 97

(list; graph; refs; listen; history; text; internal format)

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