A098936 - OEIS

A098936

Numbers n such that the partition function A000041(k) is even and odd the same number of times for 0 <= k <= n.

6671, 6673, 7931, 7941, 7945, 7947, 7949, 7951, 7953, 7957, 7959, 7973, 7979, 8113, 8117, 8125, 8127, 8135, 8139, 8141, 8183, 8193, 8195, 8199, 8201, 8205, 8207, 8211, 8213, 8215, 8217, 8269, 8325, 8331, 8335, 8341, 8343, 8345, 8351, 8353, 8357, 8359

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OFFSET

1,1

REFERENCES

Berndt, Bruce C.; Yee, Ae Ja; Zaharescu, Alexandru New theorems on the parity of partition functions. J. Reine Angew. Math. 566 (2004), 91-109. MR2039324

LINKS

Table of n, a(n) for n=1..42.

MATHEMATICA

Flatten[Position[Accumulate[Table[If[EvenQ[PartitionsP[n]], 1, -1], {n, 0, 8400}]], _?(#==0&)]]-1 (* Harvey P. Dale, Aug 25 2020 *)

PROG

(PARI) lista(n) = {ne = 0; no = 0; for (i=0, n, if (numbpart(i) % 2, no++, ne++); if (ne == no, print1(i, ", "); ); ); } \\ Michel Marcus, Aug 15 2013

CROSSREFS

Cf. A000041.

Sequence in context: A043516 A046410 A326811 * A345601 A345860 A206008

Adjacent sequences: A098933 A098934 A098935 * A098937 A098938 A098939

KEYWORD

nonn

AUTHOR

Kevin O'Bryant, Oct 20 2004

STATUS

approved