A083064
Square number array T(n,k) = (k*(k+2)^n+1)/(k+1) read by antidiagonals.
Original entry on oeis.org
1, 1, 1, 1, 2, 1, 1, 3, 5, 1, 1, 4, 11, 14, 1, 1, 5, 19, 43, 41, 1, 1, 6, 29, 94, 171, 122, 1, 1, 7, 41, 173, 469, 683, 365, 1, 1, 8, 55, 286, 1037, 2344, 2731, 1094, 1, 1, 9, 71, 439, 2001, 6221, 11719, 10923, 3281, 1, 1, 10, 89, 638, 3511, 14006, 37325, 58594, 43691, 9842, 1
Offset: 0
Rows begin:
1 1 1 1 1 1 1 1 1 ...
1 2 5 14 41 122 365 1094 3281 ... A007051
1 3 11 43 171 683 2731 10923 43691 ... A007583
1 4 19 94 469 2344 11719 58594 292969 ... A083065
1 5 29 173 1037 6221 37325 223949 1343693 ... A083066
1 6 41 286 2001 14006 98041 686286 4804001 ... A083067
1 7 55 439 3511 28087 224695 1797559 14380471 ... A083068
1 8 71 638 5741 51668 465011 4185098 37665881 ... A187709
1 9 89 889 8889 88889 888889 8888889 88888889 ... A059482
1 10 109 1198 13177 144946 1594405 17538454 192922993 ... A199760, etc.
Column 2: A000027;
column 3: A028387;
column 4: A083074;
column 5: A125082;
column 6: A125083.
Diagonals:
1, 2, 11, 94, 1037, 14006, ... A083069;
1, 3, 19, 173, 2001, 28087, ... A083071;
1, 4, 29, 286, 3511, 51668, ... A083072;
1, 5, 41, 439, 5741, 88889, ... A083073;
1, 5, 43, 469, 6221, 98041, ... A083070;
1, 14, 171, 2344, 37325, 686286, ... A191690.
Triangle begins:
1;
1, 1;
1, 2, 1;
1, 3, 5, 1;
1, 4, 11, 14, 1;
1, 5, 19, 43, 41, 1;
1, 6, 29, 94, 171, 122, 1; etc.
Cf. rows:
A007051,
A007583,
A059482,
A083065 -
A083068,
A187709,
A199760; columns:
A000027,
A028387,
A083074,
A125082,
A125083; diagonals:
A083069 -
A083073,
A191690.
A173180
Numbers k such that k^5-k^4-k^3-k^2-k-1 is prime.
Original entry on oeis.org
4, 6, 8, 14, 18, 20, 24, 26, 28, 32, 40, 42, 50, 58, 62, 68, 72, 100, 104, 120, 122, 140, 150, 174, 184, 192, 210, 234, 240, 260, 266, 278, 288, 300, 306, 326, 346, 366, 404, 432, 444, 460, 464, 466, 470, 484, 488, 512, 516, 526, 538, 556, 562, 564, 570, 584
Offset: 1
-
filter:= k -> isprime( k^5-k^4-k^3-k^2-k-1):
select(filter, 2*[$1..500]); # Robert Israel, Apr 11 2019
-
f[n_]:=n^5-n^4-n^3-n^2-n-1;Select[Range[7! ],PrimeQ[f[ #1]]&]
Select[Range[2,600,2],PrimeQ[#^5-Total[#^Range[0,4]]]&] (* Harvey P. Dale, Sep 26 2023 *)
A237640
Numbers n of the form p^5 - Phi_5(p) (for prime p) such that n^5 - Phi_5(n) is also prime.
Original entry on oeis.org
122, 340352, 830519696, 11479086422, 266390469692, 310503441398, 2718130415306, 14837993872846, 59538248604388, 889257663626476, 2496623039993996, 6427431330617746, 7120028814392596, 10777302002014868, 12942591289426088, 24039736320940828
Offset: 1
122 = 3^5-3^4-3^3-3^2-3^1-1 (3 is prime) and 122^5-122^4-122^3-122^2-122^1-1 = 26803717321 is prime. Thus, 122 is a member of this sequence.
A238445
Primes p such that f(f(p)) is prime, where f(x) = x^5-x^4-x^3-x^2-x-1.
Original entry on oeis.org
3, 13, 61, 103, 193, 199, 307, 431, 569, 977, 1201, 1451, 1481, 1609, 1669, 1889, 2371, 2381, 2711, 2819, 3083, 3469, 4289, 4337, 4567, 5231, 5501, 6733, 7043, 7253, 7351, 7549, 8707, 9257, 9497, 10039, 10687, 11491, 12227, 12517, 12941, 13397
Offset: 1
3 is prime. 3^5-3^4-3^3-3^2-3-1 = 122 and 122^5-122^4-122^3-122^2-122-1 = 26803717321 is a prime number. Thus, 3 is a member of this sequence.
Showing 1-4 of 4 results.
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