A100474 a(1) = 1; a(n) is the smallest integer such that a(n) + a(n-1) has the first n distinct prime factors not used before in this construction.

1, 5, 380, 96197, 58546472, 42588477041, 42945524659398, 62170660055541623, 133274332258941430724, 322874181064180119947025, 950049250593734799731643802, 4193776877793643794299905615515

Offset

1,2

Comments

a(11) is the first semiprime in the sequence. What is the next? After a(2) = 5, is there another prime?

Links

Table of n, a(n) for n=1..12.

Formula

a(n) + a(n-1) = primorial(triangular(n)-1)/primorial(triangular(n-1)-1) = A002110(A000217(n)-1)/A002110(A000217(n-1)-1)

Example

a(2) = 5 because 5 + a(1) = 2 * 3.
a(3) = 380 because 380 + a(2) = 5 * 7 * 11.
a(4) = 96197 because 96197 + a(3) = 13 * 17 * 19 * 23 (note that 96197 is coincidentally the 3-brilliant 19 * 61 * 83).

Crossrefs

Cf. A000040, A001358, A002110, A000217.

Sequence in context: A261433 A206386 A198902 * A152438 A060506 A302394

Adjacent sequences: A100471 A100472 A100473 * A100475 A100476 A100477

Keyword

easy,nonn

Author

Jonathan Vos Post, Nov 22 2004

Extensions

Offset and formula corrected by Giovanni Resta, Jun 17 2016

Status

approved