A376488
a(n) is the least k such that A375422(k) = n.
Original entry on oeis.org
1, 2, 4, 9, 13, 16, 18, 21, 71, 72, 75, 77, 79, 82, 84, 85, 88, 93, 95, 97, 470, 472, 475, 497, 500, 511, 515, 526, 529, 544, 557, 2618, 2738, 2743, 2744, 2749, 2761, 2762, 2827, 2832, 2835, 2862, 2890, 2892, 2895, 2896, 2901, 2902, 2910, 2932, 2938, 2955
Offset: 1
A357345
E.g.f. satisfies A(x) = -log(1 - x * exp(A(x))) * exp(3 * A(x)).
Original entry on oeis.org
0, 1, 9, 173, 5226, 216564, 11429592, 733443990, 55447217928, 4826605609584, 475490102407200, 52299789903627408, 6353202640983827472, 844774875973448667792, 122040471544637793494760, 19034141943046836097099080, 3187643959565686909679931648
Offset: 0
-
a(n) = sum(k=1, n, (n+3*k)^(k-1)*abs(stirling(n, k, 1)));
A381110
a(n) is the maximum number of points from the set {(k, f(k)); k = 0..n} belonging to a straight line passing through the point (n, f(n)), where f(n) = A060143(n) = floor(n/phi) and phi is the golden ratio (sqrt(5)+1)/2.
Original entry on oeis.org
1, 2, 2, 2, 3, 3, 4, 3, 5, 3, 4, 4, 4, 5, 3, 5, 4, 4, 6, 4, 5, 5, 5, 6, 5, 6, 7, 6, 5, 6, 7, 6, 7, 5, 7, 8, 6, 8, 6, 7, 9, 6, 9, 7, 6, 10, 6, 7, 8, 7, 11, 7, 7, 9, 7, 12, 7, 8, 10, 8, 8, 8, 8, 11, 8, 9, 9, 9, 9, 8, 9, 10, 9, 10, 9, 10, 11, 8, 10, 10, 10, 11, 8
Offset: 0
A375423
a(1) = 1; for any n > 1, a(n) is the maximum number of points from the set {(k, a(k)), k = 1..n-1} belonging to a straight line passing through the point (n-1, a(n-1)).
Original entry on oeis.org
1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 3, 5, 5, 4, 4, 5, 3, 6, 4, 6, 3, 7, 5, 4, 7, 4, 8, 4, 9, 5, 5, 6, 4, 10, 6, 4, 11, 6, 5, 7, 3, 8, 3, 9, 4, 12, 3, 10, 4, 13, 3, 11, 5, 8, 3, 12, 6, 6, 7, 4, 14, 4, 15, 4, 16, 4, 17, 4, 18, 5, 9, 4, 19, 4, 20, 5, 10, 3, 13, 3
Offset: 1
The first terms, alongside an appropriate set of points, are:
n a(n) Points
-- ---- -----------------------------------
1 1 N/A
2 1 (1,1)
3 2 (1,1), (2,1)
4 2 (1,1), (3,2)
5 2 (1,1), (4,2)
6 3 (3,2), (4,2), (5,2)
7 3 (2,1), (4,2), (6,3)
8 3 (1,1), (4,2), (7,3)
9 3 (2,1), (5,2), (8,3)
10 4 (6,3), (7,3), (8,3), (9,3)
11 4 (1,1), (4,2), (7,3), (10,4)
12 4 (2,1), (5,2), (8,3), (11,4)
13 3 (4,2), (8,3), (12,4)
14 5 (6,3), (7,3), (8,3), (9,3), (13,3)
15 5 (2,1), (5,2), (8,3), (11,4), (14,5)
A376497
a(n) is the maximum number of points from the set {(prime(k), prime(k+1)), k = 1..n} belonging to a straight line passing through the point (prime(n), prime(n+1)) (where prime(k) denotes the k-th prime number).
Original entry on oeis.org
1, 2, 2, 2, 3, 2, 4, 3, 3, 5, 2, 4, 6, 5, 3, 4, 7, 5, 6, 8, 6, 7, 7, 3, 8, 9, 9, 10, 10, 3, 11, 8, 11, 3, 12, 9, 10, 12, 11, 12, 13, 3, 14, 13, 15, 3, 2, 14, 16, 15, 13, 17, 3, 14, 15, 16, 18, 17, 16, 19, 4, 4, 17, 20, 18, 3, 18, 5, 21, 19, 19, 3, 20, 21, 20
Offset: 1
The first terms, alongside an appropriate set of points, are:
n a(n) Points
-- ---- ------------------------------------------------
1 1 (2,3)
2 2 (2,3), (3,5)
3 2 (3,5), (5,7)
4 2 (5,7), (7,11)
5 3 (3,5), (5,7), (11,13)
6 2 (7,11), (13,17)
7 4 (3,5), (5,7), (11,13), (17,19)
8 3 (7,11), (13,17), (19,23)
9 3 (3,5), (13,17), (23,29)
10 5 (3,5), (5,7), (11,13), (17,19), (29,31)
11 2 (23,29), (31,37)
12 4 (7,11), (13,17), (19,23), (37,41)
13 6 (3,5), (5,7), (11,13), (17,19), (29,31), (41,43)
14 5 (7,11), (13,17), (19,23), (37,41), (43,47)
15 3 (23,29), (31,37), (47,53)
16 4 (23,29), (31,37), (47,53), (53,59)
Showing 1-5 of 5 results.
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