A002960 -id:A002960 - cp's OEIS frontend

A274004 First differences of A002960.

3, 3, 4, 5, 5, 6, 6, 7, 7, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 17, 17, 18, 18, 19, 19, 20, 20, 21, 21, 22, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 28, 28, 29, 29, 30, 30, 31, 31, 32, 33, 33, 34, 34, 35, 35

Offset: 1

Alisa Ediger, Jun 06 2016

nonn

The squared sieve sequence (A002960) increases by one, beginning with three, every two integers except a difference of 2^n appears only once. This is the sequence of first differences. This has not yet been proven in the general case.

Cf. A002960, A274089.

Rest@ Differences@ Map[First, NestWhileList[Function[w, {First@ #, Rest@ #} &@ Delete[Last@ w, #] &@ Map[{#} &, Reverse@ Range[Floor@ Sqrt@ Length[Last@ w]]^2]], {0, Range@ 1200}, Length@ Last@ # > 1 &]] (* Michael De Vlieger, Aug 10 2016 *)

Conjecture: a(n) = A274089(n+2). - Omar E. Pol, Aug 10 2016

A274089 Numbers repeated except that powers of 2 only appear once.

Original entry on oeis.org

1, 2, 3, 3, 4, 5, 5, 6, 6, 7, 7, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 17, 17, 18, 18, 19, 19, 20, 20, 21, 21, 22, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 28, 28, 29, 29, 30, 30, 31, 31, 32, 33, 33, 34, 34, 35, 35, 36, 36, 37, 37, 38, 38, 39, 39, 40, 40

Offset: 1

N. J. A. Sloane, Jun 10 2016

Cf. A057716.

Conjectured to be (essentially) the first differences of A002960.

a(n) = n++; my(k=logint(n,2)); n+=k; (n + bittest(n,k+1)) >> 1; \\ Kevin Ryde, Apr 28 2024

def A274089(n): return n+(k:=n.bit_length())+bool(n+k&(1<>1 # Chai Wah Wu, Sep 05 2024

a(n) = floor(A057716(n) / 2). - Kevin Ryde, Apr 28 2024

cp's OEIS Frontend

A274004 First differences of A002960.

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