A075557 a(n) is the smallest odd prime such that (1) a(n) doesn't already appear in the sequence; (2) the n-th partial sum is divisible by n; and (3) the n-th partial sum is relatively prime to n+1.

3, 5, 7, 13, 37, 31, 23, 17, 53, 11, 251, 29, 79, 43, 73, 61, 97, 67, 107, 173, 59, 103, 199, 163, 7, 1, 149, 47, 101, 509, 89, 151, 283, 229, 271, 211, 109, 257, 113, 269, 157, 241, 331, 83, 389, 41, 313, 1543, 19, 307, 463, 373, 277, 811, 457, 137, 191, 419, 311, 197

Offset

1,1

Comments

Condition (3) is needed to ensure that a(n+1) exists.

Links

Table of n, a(n) for n=1..60.

Example

a(5)=37: The 4th partial sum is 28. 7 is the smallest odd prime that satisfies (2) (28+7=35), but 7 has already been used. 17 satisfies (1) and (2) (28+17=45), but 45+a(6) must be a multiple of 6 and the only odd prime satisfying that requirement is 3, which has already been used. 37 works (28+37=65).

Crossrefs

Sequence in context: A179633 A047933 A369433 * A244452 A057187 A163080

Adjacent sequences: A075554 A075555 A075556 * A075558 A075559 A075560

Keyword

nonn,easy

Author

Amarnath Murthy, Sep 24 2002

Extensions

Edited by David Wasserman, Jun 27 2003

Status

approved