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A375420
a(n) is the number of straight lines passing through the points (i, prime(i)) and (j, prime(j)) with i < j <= n (where prime(k) denotes the k-th prime number).
2
0, 1, 3, 4, 8, 13, 17, 20, 25, 32, 40, 48, 56, 66, 74, 84, 94, 105, 120, 135, 148, 162, 176, 191, 211, 230, 247, 267, 287, 306, 333, 361, 385, 410, 437, 462, 488, 517, 545, 571, 601, 633, 663, 696, 730, 761, 796, 836, 879, 921, 962, 1000, 1038, 1080, 1122
OFFSET
1,3
FORMULA
a(n) <= A000217(n+1).
EXAMPLE
The first terms, alongside the new lines passing through (n, prime(n)), are:
n a(n) New lines passing through (n, prime(n))
- ---- --------------------------------------------
1 0 {}
2 1 {x + 1}
3 3 {2*x - 1, 3/2*x + 1/2}
4 4 {5/3*x + 1/3}
5 8 {4*x - 9, 3*x - 4, 8/3*x - 7/3, 9/4*x - 1/4}
PROG
(PARI) { L = []; for (n = 1, #p = primes(55), print1 (#L = setunion(L, Set(vector(n-1, i, polinterpolate([i, n], [p[i], p[n]]))))", "); ); }
CROSSREFS
Sequence in context: A153339 A275989 A343562 * A033955 A327466 A049720
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Aug 14 2024
STATUS
approved