OFFSET
1,1
COMMENTS
Necessarily r is even (elementary proof by induction).
s=0 is (trivial) case of 2 and the known five Fermat primes: 2, 3, 5, 17, 257, 65537 (A092506).
Fermat prime exponents r are 0, 1, 2, 4, 8, 16.
REFERENCES
Emil Artin: Galoissche Theorie, Verlag Harri Deutsch, Zuerich, 1973
Leonard E. Dickson: History of the Theory of numbers, vol. I, Dover Publications, 2005
Paulo Ribenboim, Wilfrid Keller, Joerg Richstein: Die Welt der Primzahlen, Springer-Verlag GmbH Berlin, 2006
EXAMPLE
2^0*13^0 + 1 = 2 = prime(1) => a(1).
2^10*13^1 + 1 = 13313 = prime(1581) => a(9).
list of (r,s): (0,0), (1,0), (2,0), (4,0), (2,1), (8,0), (2,2), (8,1), (10,1), (4,3), (16,0), (14,2), (20,1), (20,3), (28,1), (10,6), (26,2), (10,9), (32,5), (40,4), (10,13), (22,10), (32,8), (48,4), (20,13), (2,18), (28,11), (50,6).
PROG
(GAP)
K:=10^7;; # to get all terms <= K.
A:=Filtered([1..K], IsPrime);;
B:=List(A, i->Factors(i-1));;
C:=[];; for i in B do if Elements(i)=[2] or Elements(i)=[2, 13] then Add(C, Position(B, i)); fi; od;
A173236:=Concatenation([2], List(C, i->A[i])); # Muniru A Asiru, Sep 10 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Feb 13 2010
STATUS
approved