The OEIS is supported by the many generous donors to the OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A355778 Numbers k such that both k and k^2 + 2 can be written as the sum of two nonzero squares. 0
 40, 68, 72, 104, 148, 180, 320, 392, 468, 544, 612, 648, 720, 788, 832, 900, 936, 968, 1040, 1044, 1156, 1192, 1256, 1300, 1332, 1508, 1732, 1796, 1800, 1832, 1872, 1940, 2056, 2196, 2308, 2336, 2372, 2448, 2664, 2696, 2740, 2804, 2848, 2880, 3060, 3200, 3280 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The terms in this sequence can be considered as a solution to the "near miss" problem which occurs frequently while solving Diophantine equations. It is known that if a number k can be written as the sum of two nonzero distinct squares then so can k^2 and k^2+1. Thus, finding numbers k such that k^2+2 satisfies the same property makes it quite interesting. LINKS Table of n, a(n) for n=1..47. EXAMPLE 40 is a term since 40 = 2^2 + 6^2 as well as 40^2 + 2 = 1602 = 9^2 + 39^2. 320 is a term since 320 = 8^2 + 16^2 as well as 320^2 + 2 = 102402 = 201^2 + 249^2. PROG (PARI) is1(n)= for( i=1, #n=factor(n)~%4, n[1, i]==3 && n[2, i]%2 && return); n && ( vecmin(n[1, ])==1 || (n[1, 1]==2 && n[2, 1]%2)); \\ A000404 isok(k) = is1(k) && is1(k^2+2); \\ Michel Marcus, Jul 18 2022 (Python) from itertools import count, islice from sympy import factorint def A355778_gen(startvalue=1): # generator of terms >= startvalue for n in count(max(startvalue, 1)): c = False for p in (f:=factorint(n)): if (q:= p & 3)==3 and f[p]&1: break elif q == 1: c = True else: if c or f.get(2, 0)&1: c = False for p in (f:=factorint(n**2+2)): if (q:= p & 3)==3 and f[p]&1: break elif q == 1: c = True else: if c or f.get(2, 0)&1: yield n A355778_list = list(islice(A355778_gen(), 30)) # Chai Wah Wu, Sep 14 2022 CROSSREFS Cf. A000290, A000404, A000415. Sequence in context: A205066 A232870 A338373 * A235283 A134216 A043156 Adjacent sequences: A355775 A355776 A355777 * A355779 A355780 A355781 KEYWORD nonn AUTHOR Angad Singh, Jul 16 2022 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 27 19:23 EDT 2023. Contains 365714 sequences. (Running on oeis4.)