OFFSET
1,8
COMMENTS
Note that this sequence is different from A232443.
Conjecture: a(n) > 0 for all n > 3. Also, a(n) = 1 only for n = 4, 5, 6, 7, 9, 10, 11, 12, 15, 16, 28, 35.
LINKS
Zhi-Wei Sun, Table of n, a(n) for n = 1..10000
Zhi-Wei Sun, Conjectures involving primes and quadratic forms, preprint, arXiv:1211.1588 [math.NT], 2012-2017.
Z.-W. Sun, On a^n+ bn modulo m, arXiv preprint arXiv:1312.1166 [math.NT], 2013-2014.
EXAMPLE
a(10) = 1 since 10 = 7 + 7 - pi(7), and 7 is an odd prime not exceeding 10.
a(11) = 1 since 11 = 5 + 11 - pi(11), and 5 and 11 are odd primes not exceeding 11.
a(15) = 1 since 15 = 13 + 5 - pi(5), and 13 and 5 are odd primes not exceeding 15.
a(28) = 1 since 28 = 17 + 19 - pi(19), and 17 and 19 are odd primes not exceeding 28.
a(35) = 1 since 35 = 29 + 11 - pi(11), and 29 and 11 are odd primes not exceeding 35.
MATHEMATICA
PQ[n_]:=n>2&&PrimeQ[n]
a[n_]:=Sum[If[PQ[n-Prime[k]+k], 1, 0], {k, 2, PrimePi[n]}]
Table[a[n], {n, 1, 100}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Nov 24 2013
STATUS
approved