A100797 For each k let k_2 be the smallest number greater than k+1 and coprime to k*(k+1) and let k_3 be the smallest number greater than k_2 and coprime to k*(k+1)*k_2. The sequence lists numbers k such that k*(k+1) + k_2*k_3 and -k*(k+1) + k_2*k_3 are prime.

1, 2, 3, 4, 5, 9, 11, 12, 15, 17, 19, 23, 26, 29, 30, 32, 33, 35, 43, 45, 61, 64, 71, 73, 75, 76, 83, 84, 85, 86, 90, 91, 95, 101, 107, 108, 110, 114, 121, 124, 132, 136, 137, 140, 142, 143, 163, 169, 175, 179, 182, 184, 198, 201, 211, 212, 219, 222, 223, 231, 234

Offset

1,2

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Example

Let k = 5: The smallest number greater than 6 and coprime to 5*6 is 7. The smallest number greater than 7 and coprime to 5*6*7 is 11. Therefore k_2 = 7 and k_3 = 11. Since 5*6 + 7*11 and -5*6 + 7*11 are both primes, 5 is a term of the sequence.

Mathematica

e = {}; For[n = 1, n < 250, n++, a = n; b = n + 1; c = n + 2; While[Not[GCD[c, n]*GCD[c, n + 1] == 1], c++ ]; d = c + 1; While[Not[GCD[d, a]*GCD[d, b]*GCD[d, c] == 1], d++ ]; If[PrimeQ[a*b + c*d], If[PrimeQ[ - a*b + c*d], AppendTo[e, n]]]]; e

Crossrefs

Sequence in context: A360687 A176008 A143827 * A139441 A333612 A362025

Adjacent sequences: A100794 A100795 A100796 * A100798 A100799 A100800

Keyword

nonn,less

Author

J. M. Bergot, May 26 2007

Extensions

Edited, corrected and extended by Stefan Steinerberger, Nov 24 2007

Status

approved