A338028 Erase the zeros of the sequence and the minus signs: what remains is A018252 (the nonprime numbers). Successive additions of the present terms placed between two zeros give the successive integers of A000040 (the prime numbers).

0, -1, -4, 6, -8, 9, 0, -10, 12, -14, 15, 0, -16, -18, 20, 21, 22, -24, 0, -25, 26, -27, -28, 30, 32, 33, -34, 0, -35, -36, -38, 39, 40, 42, 44, -45, 0, -46, -48, 49, -50, 51, -52, 54, 55, 0, -56, -57, -58, 60, 62, -63, 64, 65, 0, -66, -68, -69, 70, -72, 74, 75, 76, 77, -78, 0, -80, -81, -82, -84, 85, 86, 87, -88

Offset

1,3

Comments

The successive zeros of the sequence could be replaced by the successive primes; the sequence would then start with 2, -1, -4, 6, -8, 9, 3, -10, 12, -14, 15, 5, -16, -18, 20, 21, 22, -24, 7, -25, 26, -27, -28, 30, 32, 33, -34, 11, -35, ...

Links

Carole Dubois, Table of n, a(n) for n = 1..499

Example

2 is the result of (-1) + (-4) + 6 + (-8) + 9,
3 is the result of (-10) + 12 + (-14) + 15,
5 is the result of (-16) + (-18) + 20 + 21 + 22 + (-24),
7 is the result of (-25) + 26 + (-27) + (-28) + 30 + 32 + 33 + (-34),
11 is the result of (-35) + (-36) + (-38) + 39 + 40 + 42 + 44 + (-45).
etc.

Crossrefs

Cf. A018252, A000040.

Sequence in context: A083786 A199976 A165957 * A110750 A275589 A129808

Adjacent sequences: A338025 A338026 A338027 * A338029 A338030 A338031

Keyword

sign

Author

Eric Angelini and Carole Dubois, Oct 08 2020

Status

approved