login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

"Late birds" (a(n)<a(k) for all k>n) in A268630 (= a(n)^2+a(n+1) is prime).
4

%I #5 Feb 09 2016 20:54:14

%S 0,1,3,5,6,11,14,17,26,61,62,74,77,80,101,179,191,206,209,212,269,329,

%T 341,383,401,404,425,455,458,461,467,491,557,560,581,605,614,668,680,

%U 731,734,824,869,875,890,893,911,923,935,944,959,1031,1064,1097,1118,1130,1151,1154,1316,1322,1328,1349

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

%C 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.

%C 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.

%H M. F. Hasler, <a href="/A268495/b268495.txt">Table of n, a(n) for n = 0..428</a>

%o (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))}

%K nonn

%O 0,3

%A _M. F. Hasler_, Feb 09 2016