A126040
a(n) is the largest prime < 12*a(n-1) for n > 1, with a(1) = 2.
Original entry on oeis.org
2, 23, 271, 3251, 38993, 467903, 5614831, 67377943, 808535311, 9702423659, 116429083879, 1397149006493, 16765788077893, 201189456934709, 2414273483216333, 28971281798595971, 347655381583151639, 4171864578997819661, 50062374947973835871, 600748499375686030387, 7208981992508232364591
Offset: 1
A229609
Array: each row starts with the least prime not in a previous row, and each prime p in a row is followed by the greatest prime < 3*p.
Original entry on oeis.org
2, 5, 3, 13, 7, 11, 37, 19, 31, 17, 109, 53, 89, 47, 23, 317, 157, 263, 139, 67, 29, 947, 467, 787, 409, 199, 83, 41, 2837, 1399, 2357, 1223, 593, 241, 113, 43, 8501, 4177, 7069, 3659, 1777, 719, 337, 127, 59, 25471, 12527, 21193, 10973, 5323, 2153, 1009
Offset: 1
Northwest corner:
2, 5, 13, 37, 109, 317, ...
3, 7, 19, 53, 157, 467, ...
11, 31, 89, 263, 787, 2357, ...
17, 47, 139, 409, 1223, 3659, ...
23, 67, 199, 593, 1777, 5323, ...
29, 83, 241, 719, 2153, 6451, ...
-
seqL = 14; arr1[1] = {2}; Do[AppendTo[arr1[1], NextPrime[3*Last[arr1[1]], -1]], {seqL}]; Do[tmp = Union[Flatten[Map[arr1, Range[z]]]]; arr1[z] = {Prime[NestWhile[# + 1 &, 1, PrimePi[tmp[[#]]] - # == 0 &]]}; Do[AppendTo[arr1[z], NextPrime[3*Last[arr1[z]], -1]], {seqL}], {z, 2, 22}]; m = Map[arr1, Range[22]]; m // TableForm
t = Table[m[[n - k + 1]][[k]], {n, 12}, {k, n, 1, -1}] // Flatten (* Peter J. C. Moses, Sep 26 2013 *)
Incorrect comment deleted by
Peter Munn, Aug 15 2017
A124368
Largest prime < 1000000*a(n-1), a(1)=2.
Original entry on oeis.org
2, 1999993, 1999992999889, 1999992999888999961, 1999992999888999960999949, 1999992999888999960999948999991, 1999992999888999960999948999990999917, 1999992999888999960999948999990999916999963, 1999992999888999960999948999990999916999962999947
Offset: 1
-
NestList[NextPrime[1000000#,-1]&,2,10] (* Harvey P. Dale, Jul 21 2021 *)
A126034
a(n) is largest prime < 6*a(n-1) for n > 1 with a(1) = 2.
Original entry on oeis.org
2, 11, 61, 359, 2153, 12917, 77491, 464941, 2789629, 16737761, 100426553, 602559311, 3615355859, 21692135119, 130152810703, 780916864207, 4685501185193, 28113007111153, 168678042666907, 1012068256001351, 6072409536008087, 36434457216048503, 218606743296291011
Offset: 1
-
Nest[Append[#,NextPrime[6Last[#], -1]]&,{2},22] (* James C. McMahon, Dec 24 2024 *)
A124387
Largest prime < 2*a(n-1) written in binary, a(1)=2.
Original entry on oeis.org
10, 11, 101, 111, 1101, 10111, 101011, 1010011, 10100011, 100111101, 1001110111, 10011101011, 100111000111, 1001110001011, 10011011110101, 100110111100001, 1001101110111101, 10011011101010011, 100110111010011101, 1001101110100011111, 10011011101000111011
Offset: 1
-
NestList[FromDigits[IntegerDigits[NextPrime[FromDigits[IntegerDigits[ 2#], 2],-1],2]]&,10,20] (* Harvey P. Dale, Sep 26 2015 *)
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