cp's OEIS Frontend

A385614 Numbers of the form x^x + y^y, 1 < x < y.

%I A385614 #37 Jul 15 2025 08:29:04
%S A385614 31,260,283,3129,3152,3381,46660,46683,46912,49781,823547,823570,
%T A385614 823799,826668,870199,16777220,16777243,16777472,16780341,16823872,
%U A385614 17600759,387420493,387420516,387420745,387423614,387467145,388244032,404197705,10000000004
%N A385614 Numbers of the form x^x + y^y, 1 < x < y.
%C A385614 Terms are all combinations of 1 < x < y ordered by increasing y then increasing x, since the largest of one y is strictly less than the smallest of the next: (y-1)^(y-1) + y^y < 2^2 + (y+1)^(y+1) for y >= 3. - _Kevin Ryde_, Jul 06 2025
%H A385614 Sean A. Irvine, <a href="/A385614/b385614.txt">Table of n, a(n) for n = 1..1000</a>
%F A385614 a(n) = x^x + y^y where x=A131818(n+1) and y=A133196(n). - _Kevin Ryde_, Jul 06 2025
%e A385614 31 is in the sequence because 31 = 2^2 + 3^3.
%o A385614 (PARI) a(n) = my(r,s=sqrtint((n-1)<<1,&r), x=2 + if(r<s, r+s, r-s)>>1, y=3 + s-(r<s)); x^x+y^y; \\ _Kevin Ryde_, Jul 06 2025
%o A385614 (Python)
%o A385614 from math import isqrt, comb
%o A385614 def A385614(n):
%o A385614     y = (m:=isqrt(k:=n<<1))+(k>m*(m+1))+2
%o A385614     x = n-comb(y-2,2)+1
%o A385614     return x**x+y**y # _Chai Wah Wu_, Jul 07 2025
%Y A385614 Cf. A000312, A173054, A385232.
%K A385614 nonn,easy
%O A385614 1,1
%A A385614 _Sean A. Irvine_, Jul 04 2025