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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. 0
1, 5, 380, 96197, 58546472, 42588477041, 42945524659398, 62170660055541623, 133274332258941430724, 322874181064180119947025, 950049250593734799731643802, 4193776877793643794299905615515 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 30 07:52 EDT 2022. Contains 357104 sequences. (Running on oeis4.)