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A128490
Integers of the form (p(n+1)*p(n) - 1)/(p(n+1) - p(n)) where p(n) denotes the n-th prime.
1
5, 7, 17, 19, 55, 71, 109, 111, 161, 191, 379, 415, 449, 505, 521, 681, 881, 961, 1025, 1079, 1189, 1231, 1639, 1799, 2071, 2449, 2591, 2755, 2991, 3079, 3457, 3499, 3921, 3951, 4159, 4265, 4815, 5161, 5201, 5831, 6049, 6425, 6805, 9281, 9505, 9521, 10751
OFFSET
1,1
EXAMPLE
[5*3-1]/(5-2) = 14/2 = 7
[7*5-1]/(7-5) = 34/2 = 17
[11*7-1]/(11-7) = 76/4 = 19
MAPLE
P:=proc(n) local i, j, k; for i from 1 by 1 to n do j:=(ithprime(i+1)*ithprime(i)-1)/(ithprime(i+1)-ithprime(i)); if j=trunc(j) then print(j); fi; od; end: P(1000);
MATHEMATICA
Select[(Times@@#-1)/(#[[2]]-#[[1]])&/@Partition[Prime[Range[100]], 2, 1], IntegerQ]//Sort (* Harvey P. Dale, Jul 29 2024 *)
CROSSREFS
Cf. A128491.
Sequence in context: A075304 A168245 A242929 * A023519 A023517 A128491
KEYWORD
easy,nonn
AUTHOR
STATUS
approved