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

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

1,2

Comments

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

Links

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

Example

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)

Mathematica

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 *)

Crossrefs

Cf. A109919, A109920, A063934, A060863.

Cf. A054265.

Sequence in context: A066246 A198370 A173517 * A139637 A307734 A363346

Adjacent sequences: A109918 A109919 A109920 * A109922 A109923 A109924

Keyword

easy,nonn

Author

Amarnath Murthy, Jul 16 2005

Extensions

More terms from David Wasserman, Aug 15 2005

Status

approved