OFFSET
1,1
COMMENTS
Conjecture: Each member of this sequence can be used as an initial value for Inkeri's primality test for Fermat numbers.
Inkeri's primality test for Fermat numbers: Fermat's number F_{m}=2^2^m+1 (m => 2) is prime if and only if F_{m} divides the term v_{2^m-2} of the series v_{0}=8 , v_{i}=(v_{i-1})^2-2 .
REFERENCES
K. Inkeri, Tests for primality, Ann. Acad. Sci. Fenn., A I 279, 119 (1960).
LINKS
Pedja Terzic, Initial values of Inkeri's primality test for Fermat numbers, Math StackExchange, May 2018.
MATHEMATICA
b=RecurrenceTable[{a[1]==8, a[2]==488, a[n]==62a[n-1]-a[n-2]}, a, {n, 12}]; c= RecurrenceTable[{a[1]==22, a[2]==10582, a[n]==482a[n-1]-a[n-2]}, a, {n, 12}]; Join[ b, c]//Union (* Harvey P. Dale, May 05 2022 *)
PROG
(PARI) InitialValues(n)= {l=[8, 22, 488, 10582]; b1=8; b2=488; i=3; while(i<=n, b=62*b2-b1; l=concat(l, b); b1=b2; b2=b; i++); c1=22; c2=10582; j=3; while(j<=n, c=482*c2-c1; l=concat(l, c); c1=c2; c2=c; j++); print(vecsort(l))}
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Pedja Terzic, May 07 2018
STATUS
approved