A304177 Union of sequences b and c defined by: b(1)=8, b(2)=488, b(n)=62*b(n-1) - b(n-2) and c(1)=22, c(2)=10582, c(n)=482*c(n-1) - c(n-2).

8, 22, 488, 10582, 30248, 1874888, 5100502, 116212808, 2458431382, 7203319208, 446489578088, 1184958825622, 27675150522248, 571147695518422, 1715412842801288, 106327921103157608, 275292004281053782, 6590615695552970408, 132690174915772404502, 408511845203181007688

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

Table of n, a(n) for n=1..20.

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

Cf. A018844, A000215.

Sequence in context: A362825 A117613 A215740 * A306834 A109271 A029755

Adjacent sequences: A304174 A304175 A304176 * A304178 A304179 A304180

Keyword

easy,nonn

Author

Pedja Terzic, May 07 2018

Status

approved