A134207 a(0) = 2; for n > 0, a(n) = the smallest prime which is > a(n-1) such that a(n-1) + a(n) is a multiple of n.

2, 3, 5, 7, 13, 17, 19, 23, 41, 67, 73, 103, 113, 173, 191, 199, 233, 277, 281, 479, 521, 571, 617, 809, 823, 827, 863, 919, 929, 1217, 1303, 1487, 1489, 1613, 1753, 2027, 2113, 2179, 2267, 2647, 2713, 3109, 3191, 3259, 3517, 3593, 3767, 3847, 3881, 4057

Offset: 0

Author

Leroy Quet, Oct 14 2007

Keywords

• nonn

Examples

			The primes that are > a(8)=41 form the sequence 43,47,53,59,61,67,71,... Of these, 67 is the smallest that when added to a(8)=41 gets a multiple of 9 -- 41+67 = 108 = 9*12. (41+p is not divisible by 9 for p = any prime which is > 41 and is < 67.) So a(9) = 67.
		

Links

• Eric M. Schmidt, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A134204, A134208, A134209.

Programs

Mathematica

a = {2}; For[n = 1, n < 100, n++, i = 1; While[Not[Mod[a[[ -1]] + Prime[PrimePi[a[[ -1]]] + i], n] == 0], i++ ]; AppendTo[a, Prime[PrimePi[a[[ -1]]] + i]]]; a (* Stefan Steinerberger, Oct 17 2007 *)

Sage

def A134207(max) :
    res = [2]; p = 3
    for n in range(1,max+1) :
        while (res[n-1] + p) % n != 0 : p = next_prime(p)
        res.append(p); p = next_prime(p)
    return res # Eric M. Schmidt, May 23 2013

Extensions

More terms from Stefan Steinerberger, Oct 17 2007