A268495 "Late birds" (a(n)<a(k) for all k>n) in A268630 (= a(n)^2+a(n+1) is prime).

0, 1, 3, 5, 6, 11, 14, 17, 26, 61, 62, 74, 77, 80, 101, 179, 191, 206, 209, 212, 269, 329, 341, 383, 401, 404, 425, 455, 458, 461, 467, 491, 557, 560, 581, 605, 614, 668, 680, 731, 734, 824, 869, 875, 890, 893, 911, 923, 935, 944, 959, 1031, 1064, 1097, 1118, 1130, 1151, 1154, 1316, 1322, 1328, 1349

Offset

0,3

Comments

See A268494 for the corresponding indices, A268496-A268497 for records. 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, f="/tmp/b268495.txt", c=0, a=0, u=[a-1])={for(n=1, n, a==u[1]+1&&if(f, write(f, c++-1, " "a), print1(a", ")); 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: A326310 A047443 A173593 * A127577 A280590 A356709

Adjacent sequences: A268492 A268493 A268494 * A268496 A268497 A268498

Keyword

nonn

Author

M. F. Hasler, Feb 09 2016

Status

approved