A109919 -id:A109919 - cp's OEIS frontend

A109920 a(1) = 1, then LCM of consecutive composite numbers sandwiched between primes.

1, 2, 1, 3, 4, 5, 6, 7, 360, 11, 12, 13, 1680, 17, 18, 19, 4620, 23, 491400, 29, 30, 31, 1884960, 37, 29640, 41, 42, 43, 45540, 47, 12994800, 53, 45821160, 59, 60, 61, 89369280, 67, 164220, 71, 72, 73, 211110900, 79, 265680, 83, 195878760, 89

Offset: 1

Amarnath Murthy, Jul 16 2005

Cf. A109919.

A109920 := proc(n) local p; if n mod 2 = 0 then ithprime(n/2) ; elif n = 1 then 1 ; else p := ithprime((n-1)/2) ; lcm(seq(i,i=p+1..nextprime(p)-1)) ; fi ; end: for n from 1 to 80 do printf("%d, ",A109920(n)) ; od ; # R. J. Mathar, May 02 2007

a(2n) = prime(n) a(2n+1)= LCM of composite numbers between prime(n) and prime(n+1). a(1) = a(3) = 1 by choice.

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

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A109920 a(1) = 1, then LCM of consecutive composite numbers sandwiched between primes.

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

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