A109920 -id:A109920 - cp's OEIS frontend

A109919 a(1) = 1, then product of consecutive composite numbers sandwiched between primes.

1, 2, 1, 3, 4, 5, 6, 7, 720, 11, 12, 13, 3360, 17, 18, 19, 9240, 23, 11793600, 29, 30, 31, 45239040, 37, 59280, 41, 42, 43, 91080, 47, 311875200, 53, 549853920, 59, 60, 61, 1072431360, 67, 328440, 71, 72, 73, 2533330800, 79, 531360, 83, 4701090240, 89

Offset: 1

Amarnath Murthy, Jul 16 2005

a(1) = a(3) = 1 as empty product is defined to be 1.

The odd numbered terms are in A061214. - T. D. Noe, Oct 02 2012

Cf. A109920.
Cf. A072472.
Cf. A061214 (product of composite numbers between primes).

A109919 := proc(n) local p; if n mod 2 = 0 then ithprime(n/2) ; elif n = 1 then 1 ; else p := ithprime((n-1)/2) ; mul(i,i=p+1..nextprime(p)-1) ; fi ; end: for n from 1 to 80 do printf("%d, ",A109919(n)) ; od ; # R. J. Mathar, May 02 2007

a(2n) = prime(n) and a(2n+1)= product of composite numbers between prime(n) and prime(n+1).

a(2n) = A000040(n). a(2n+1) = A072472(n)/A000040(n+1). - R. J. Mathar, May 02 2007

More terms from R. J. Mathar, May 02 2007

A109921 a(2n) = prime(n). a(2n+1) = sum of composite numbers between prime(n) and prime(n+1). We define a(1) = 1.

Original entry on oeis.org

1, 2, 0, 3, 4, 5, 6, 7, 27, 11, 12, 13, 45, 17, 18, 19, 63, 23, 130, 29, 30, 31, 170, 37, 117, 41, 42, 43, 135, 47, 250, 53, 280, 59, 60, 61, 320, 67, 207, 71, 72, 73, 380, 79, 243, 83, 430, 89, 651, 97, 297, 101, 102, 103, 315, 107, 108, 109, 333, 113, 1560, 127, 387, 131

Offset: 1

Amarnath Murthy, Jul 16 2005

1 together with the sum of consecutive composites between primes interleaved with the primes. - Omar E. Pol, Oct 01 2012

			Contribution from _Omar E. Pol_, Oct 06 2012 (Start):
a(1) = 1, by definition. Also 1 is the first nonprime.
a(2) = 2, the first prime.
a(3) = 0, the sum of composite numbers between 2 and 3.
a(4) = 3, the second prime.
a(5) = 4, the sum of the composite numbers between 3 and 5.
a(6) = 5, the third prime.
a(7) = 6, the sum of the composite numbers between 5 and 7.
a(8) = 7, the fourth prime.
a(9) = 27, the sum of the composite numbers between 7 and 11, since 8+9+10 = 27.
a(10) = 11, the fifth prime.
(End)

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A109919, A109920, A063934, A060863.

Cf. A054265.

Join[{1},With[{nn=40},Riffle[Prime[Range[nn]],Table[Total[Range[Prime[n]+1,Prime[n+1]-1]],{n,nn}]]]] (* Harvey P. Dale, Jul 16 2023 *)

More terms from David Wasserman, Aug 15 2005

cp's OEIS Frontend

A109919 a(1) = 1, then product of consecutive composite numbers sandwiched between primes.

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