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

Author

Zak Seidov, Dec 29 2011

Keywords

• nonn

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.

Examples

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

Crossrefs

Cf. A203069.

Programs

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 *)