1,1

Comments from Karsten Meyer (arbol01(AT)gmx.de), Oct 07 2007: (Start) Each term n=a*b of the sequence is at least a Fermat pseudoprime to the two bases a1 and a2 which have the property that |p*a - q*b| = 2 and a is the number between p*a and q*b. There are no more bases of this form below of the number n.

There may be exists other bases below the number n, but just two bases have the property that they a direct neigbours of a multiple of a and a multiple of b. For example, 39=3*13 is a Fermat pseudoprime to the bases 14 and 25 because 14 is the number between 13 and 3*5 and 25 is the number between 3*8 and 2*13.

91=7*13 is a Fermat pseudoprime to the bases 27 and 64 because 27 is the number between 2*13 and 4*7 and 64 is the number between 9*7 and 5*13. For 91 exists although the bases 3, 4, 9, 10, 12, 16, 17, 22, 23, 25, 29, 30, 36, 38, 40, 43, 48, 51, 53, 55, 61, 62, 66, 68, 69, 74, 75, 79, 81, 82, 87, 88. But neither of them lies between a multiple of 7 and a multiple of 13. (End)

Subset of A098905 (which contains in addition A046390 and numbers like 255255, 285285, 345345, 373065 etc). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 13 2008]

A001221 := proc(n) nops(numtheory[factorset](n)) ; end: isA046388 := proc(n) RETURN( (n mod 2 = 1) and (A001221(n) = 2) ); end: for n from 1 to 840 do if isA046388(n) then printf("%d, ", n) ; fi; od: [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 13 2008]

Cf. A046315, A046404, A024556, A056913.

Sequence in context: A070537 A070005 A061346 this_sequence A098905 A024556 A146166

Adjacent sequences: A046385 A046386 A046387 this_sequence A046389 A046390 A046391

nonn

Patrick De Geest (pdg(AT)worldofnumbers.com), Jun 15 1998.

Inserted 45, 63, 75, 99, 117, 135 etc. by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 13 2008