A209882 Smallest k>=0 such that n*(n+1)-(2*k+1) and n*(n+1)+(2*k+1) are both noncomposite numbers, or -1 if no such k exists.

0, 0, 0, 1, 0, 0, 1, 0, 3, 1, 2, 3, 4, 6, 0, 4, 12, 2, 10, 0, 0, 1, 2, 0, 1, 12, 2, 7, 3, 5, 10, 2, 14, 1, 11, 14, 16, 0, 3, 13, 0, 2, 7, 3, 8, 25, 6, 2, 4, 0, 2, 22, 12, 0, 19, 5, 3, 85, 0, 8, 7, 8, 9, 34, 3, 0, 46, 14, 15, 1, 17, 11, 7, 9, 5, 4, 33, 5, 1, 5, 30, 13, 2, 5, 61, 2, 6, 4, 0, 9, 37, 8, 2, 34, 8, 14, 7, 20, 14, 16

Offset

1,9

Links

Table of n, a(n) for n=1..100.

Example

a(1) = 0 because 1*(1+1)-(2*0+1)=1 and 1*(1+1)+(2*0+1)=3 are both noncomposite numbers.
a(2) = 0 because 2*(2+1)-(2*0+1)=5 and 2*(2+1)+(2*0+1)=7 are both noncomposite numbers.
a(3) = 0 because 3*(3+1)-(2*0+1)=11 and 3*(3+1)+(2*0+1)=13 are both noncomposite numbers.
a(4) = 1 because 4*(4+1)-(2*1+1)=17 and 4*(4+1)+(2*1+1)=23 are both noncomposite numbers.

Prog

(PARI) isc(c) = (c>1) && !isprime(c);
a(n) = my(k=0); while (isc(n*(n+1)-(2*k+1)) || isc(n*(n+1)+(2*k+1)), k++); k; \\ Michel Marcus, Oct 16 2025

Crossrefs

Cf. A002378, A008578.

Sequence in context: A110063 A260313 A050056 * A336233 A325845 A260116

Adjacent sequences: A209879 A209880 A209881 * A209883 A209884 A209885

Keyword

sign

Author

Gerasimov Sergey, Mar 14 2012

Extensions

Corrected by R. J. Mathar, Mar 24 2012

Status

approved