A268495 "Late birds" (a(n)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

Author

M. F. Hasler, Feb 09 2016

Keywords

• nonn

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

Programs

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))}