OFFSET
1,2
COMMENTS
This sequence is a variant of A332941.
This sequence is infinite:
- suppose that the first n terms are known,
- let M = max_{k <= n} a(k) XOR ... XOR a(n),
- let k be such that M < 2^k,
- as there are prime gaps of any size,
we can choose an interval of the form [m*2^k..(m+1)*2^k] without prime numbers,
- hence a(n+1) <= m*2^k, QED.
LINKS
Rémy Sigrist, Table of n, a(n) for n = 1..511
Rémy Sigrist, PARI program for A333403
EXAMPLE
The values of a(i) XOR ... XOR a(j) for i <= j <= 8 are:
i\j| 1 2 3 4 5 6 7 8
---+------------------------------
1| 1 9 8 56 57 49 48 116
2| . 8 9 57 56 48 49 117
3| . . 1 49 48 56 57 125
4| . . . 48 49 57 56 124
5| . . . . 1 9 8 76
6| . . . . . 8 9 77
7| . . . . . . 1 69
8| . . . . . . . 68
PROG
(PARI) See Links section.
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Mar 22 2020
STATUS
approved