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

0,1

Links

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

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A134204, A134208, A134209.

Sequence in context: A049567 A293048 A134204 * A133244 A077040 A153503

Adjacent sequences: A134204 A134205 A134206 * A134208 A134209 A134210

Keyword

nonn

Author

Leroy Quet, Oct 14 2007

Extensions

More terms from Stefan Steinerberger, Oct 17 2007

Status

approved