A268630 a(n)^2 + a(n+1) is prime; lexicographically earliest sequence of nonnegative integers with this property and containing no duplicates.

0, 2, 1, 4, 3, 8, 7, 10, 9, 16, 13, 12, 5, 6, 11, 18, 23, 28, 25, 22, 15, 14, 27, 32, 37, 30, 19, 36, 31, 48, 29, 40, 21, 20, 33, 34, 45, 38, 39, 46, 63, 44, 43, 24, 17, 42, 47, 58, 49, 66, 35, 52, 73, 64, 57, 50, 51, 56, 55, 54, 41, 60, 59, 76, 67, 72, 53, 70, 69, 26, 75, 68, 79, 82, 99, 86, 61, 100, 91, 88, 85, 84, 65, 102, 83, 78, 89, 90, 71, 106, 81

Offset: 0

Author

Eric Angelini and M. F. Hasler, Feb 09 2016

Keywords

• nonn

Comments

Conjectured to be a permutation of the nonnegative integers.

Terms are of alternating parity.

The sequence cannot have a fixed point other than a(0)=0 because for n>0, the terms are of parity opposite to that of their indices.

The number of distinct m-digit primes arising from the sequence appears to be bounded by the entries of A030186. The counts here for m=1 to 9 are 2,7,21,69,216,684,2162,6801,21623 compared to A030186's 2,7,22,71,228,733,2356,7573,24342. - Bill McEachen, Feb 15 2016

Links

• Zak Seidov, Table of n, a(n) for n = 0..50000
• E. Angelini, A formula for a permutation, SeqFan list, Feb. 9, 2016.

Crossrefs

Cf. A268494, A268495, A268496, A268497 for records and late birds.

Programs

Mathematica

s = {0, 2, 1, 4}; a = 4; Do[b = Mod[a, 2] + 3; While[MemberQ[s, b] || ! PrimeQ[a^2 + b], b = b + 2]; AppendTo[s, b]; a = b, {1000}]; s (* Zak Seidov, Feb 09 2016 *)

PARI

{u=[a=0]; for(n=1, 99, for(k=1, 9e9, setsearch(u,k)&&next; isprime(a*a+k)||next; print1(k","); u=setunion(u,[a=k]); break))}