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A268630 a(n)^2 + a(n+1) is prime; lexicographically earliest sequence of nonnegative integers with this property and containing no duplicates. 5
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified March 29 20:20 EDT 2020. Contains 333117 sequences. (Running on oeis4.)