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

0,2

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.

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 *)

Prog

(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))}

Crossrefs

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

Sequence in context: A294022 A076077 A152194 * A087787 A182712 A100818

Adjacent sequences: A268627 A268628 A268629 * A268631 A268632 A268633

Keyword

nonn

Author

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

Status

approved