A268494 Indices n of "late birds" (a(n)<a(k) for all k>n) in A268630 (= a(n)^2+a(n+1) is prime).

0, 2, 4, 12, 13, 14, 21, 44, 69, 76, 107, 109, 114, 127, 204, 214, 246, 249, 298, 317, 394, 402, 420, 440, 442, 477, 504, 508, 533, 550, 552, 610, 632, 647, 656, 682, 743, 745, 801, 808, 925, 943, 952, 954, 961, 966, 980, 1010, 1050, 1089, 1112, 1162, 1167, 1200, 1229, 1233, 1244, 1389, 1401, 1415, 1423, 1432, 1462

Offset

0,2

Comments

See A268495 for the corresponding values. We use offset 0 here because the first term has a special status (it's not really "late") and also because all related sequences (A268630 and A268494 - A268497) have a(0)=0 and omitting this term yields the corresponding "positive integer" variant.

Assuming that A268630 is a permutation of the nonnegative integers N (as conjectured), the characterization given in the name is equivalent to say that a(n) equals the least number not occurring earlier. The sequence defined that way is finite if and only if A268630 is not a permutation of N.

Links

M. F. Hasler, Table of n, a(n) for n = 0..428

Prog

(PARI) show(n, a=0, u=[a-1])={for(n=1, n, a==u[1]+1&&print1(n-1", "); u=setunion(u, [a]); while(#u>1&&u[2]==u[1]+1, u=u[^1]); for(k=u[1]+1, 9e9, !setsearch(u, k) && isprime(a*a+k) && (a=k) && break))}

Crossrefs

Sequence in context: A358502 A141668 A087796 * A306851 A316634 A039587

Adjacent sequences: A268491 A268492 A268493 * A268495 A268496 A268497

Keyword

nonn

Author

M. F. Hasler, Feb 09 2016

Status

approved