A203077 Alternating-parity rearrangement of natural numbers: a(n) is the smallest number such that a(n-1)^2 + a(n)^2 is odd and composite.

1, 8, 9, 2, 11, 10, 5, 12, 3, 4, 7, 6, 13, 14, 17, 16, 15, 18, 19, 22, 21, 20, 25, 30, 27, 24, 23, 26, 29, 28, 31, 32, 35, 38, 33, 34, 37, 36, 39, 42, 41, 40, 45, 44, 43, 46, 47, 50, 49, 48, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 63, 62, 61, 66, 67, 64, 65

Offset

1,2

Comments

The maximum between a(n) and the n-th integer appears to be +-6. In the first 10k terms, the distribution of differences, from -6 to 6 is: 27, 140, 1350, 7002, 1282, 168, 31. Therefore I conjecture that Lim_{n->infinity} a(n) = n.

Links

Table of n, a(n) for n=1..67.

Example

1^2 + 8^2 = 65 composite, 8^2 + 9^2 = 145 composite, 9^2 + 2^2 = 85 composite.

Mathematica

f[s_List] := Block[{k = If[ OddQ[ s[[-1]]], 2, 3], m = s[[-1]]}, While[a = k^2 + m^2; MemberQ[s, k] || PrimeQ[a] || EvenQ[a], k += 2]; Append[s, k]]; Nest[f, {1}, 70] (* Robert G. Wilson v, Jan 02 2012 *)

Crossrefs

Cf. A203069.

Sequence in context: A202623 A266261 A117914 * A339800 A197392 A021922

Adjacent sequences: A203074 A203075 A203076 * A203078 A203079 A203080

Keyword

nonn

Author

Zak Seidov, Dec 29 2011

Status

approved