OFFSET
0,1
COMMENTS
Starting at 2*n + 1, find the next odd composite number 2*n + 2*m + 1 that is relatively prime to 2*n + 1; then a(n) = m.
Since 2*n + 3 is relatively prime to 2*n + 1, and (2*n + 3)^2 is composite, a(n) <= 2*n^2 + 5*n + 4 (this is tight for n=0 and n=1).
From Andrey Zabolotskiy, Feb 13 2017: (Start)
Up to n = 10^7, a(n) are from the set [1, 2, 4, 5, 7, 8, 11, 13, 14, 16, 17, 19, 22]. First occurrence of 14 is a(99412), first occurrence of 22 is a(7225627). [Thanks to Altug Alkan for pointing out a(99412).]
a(n) = 1 iff n is in A153238.
(End)
Based on Altug Alkan's b-file, the records in this sequence are 4, 11, 17, 19, ... and occur at positions 1, 2, 8, 638, ... If the sequence is unbounded, then these two subsidiary sequences should be added to the OEIS (if they are new). - N. J. A. Sloane, Feb 13 2017
LINKS
Altug Alkan, Table of n, a(n) for n = 0..10000
EXAMPLE
When n=1, 2*n + 1 = 3, and 5, 7, 9, 11, 13, 15, 17, 19, 21, 23 are all either prime or have a common factor with 3. The next term, 25, is OK, and so a(1) = (25 - 3)/2 = 11.
MATHEMATICA
Table[m = 1; While[Nand[CoprimeQ[m, 2 n + 1], CompositeQ[2 (n + m) + 1]], m++]; m, {n, 0, 120}] (* Michael De Vlieger, Feb 18 2017 *)
PROG
(PARI) a(n) = my(k=1); while(isprime(2*n+2*k+1) || gcd(2*n+1, k) != 1, k++); k; \\ Altug Alkan, Feb 13 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Feb 12 2017
EXTENSIONS
Definition corrected by Altug Alkan, Feb 13 2017
STATUS
approved