

A078137


Numbers which can be written as sum of squares>1.


12



4, 8, 9, 12, 13, 16, 17, 18, 20, 21, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82
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OFFSET

1,1


COMMENTS

A078134(a(n))>0.
Numbers which can be written as a sum of squares of primes.  Hieronymus Fischer, Nov 11 2007
Equivalently, numbers which can be written as a sum of squares of 2 and 3. Proof for numbers m>=24: if m=4*(k+6), k>=0, then m=(k+6)*2^2; if m=4*(k+6)+1 than m=(k+4)*2^2+3^2; if m=4*(k+6)+2 then m=(k+2)*2^2+2*3^2; if m=4*(k+6)+3 then m=k*2^2+3*3^2. Clearly, the numbers a(n)<24 can also be written as sums of squares of 2 and 3. Explicit representation as a sum of squares of 2 and 3 for numbers m>23: m=c*2^2+d*3^2, where c:=((floor(m/4)  2*(m mod 4))>=0 and d:=m mod 4.  Hieronymus Fischer, Nov 11 2007


LINKS

Table of n, a(n) for n=1..70.
Index entries for sequences related to sums of squares
Eric Weisstein's World of Mathematics, Square Number.
Index entries for linear recurrences with constant coefficients, signature (2,1).


FORMULA

a(n)=n + 12 for n >= 12.  Hieronymus Fischer, Nov 11 2007


MATHEMATICA

Join[{4, 8, 9, 12, 13, 16, 17, 18, 20, 21, 22}, Range[24, 82]] (* JeanFrançois Alcover, Aug 01 2018 *)


PROG

(PARI) a(n)=if(n>11, n+12, [4, 8, 9, 12, 13, 16, 17, 18, 20, 21, 22][n]) \\ Charles R Greathouse IV, Aug 21 2011


CROSSREFS

Complement of A078135.
Cf. A000290, A078136, A078131, A001597, A025475, A078134, A078135, A078139, A090677, A134600, A134605, A134608, A134612, A134616, A134618, A134620.
Sequence in context: A297252 A296696 A297129 * A294574 A010453 A078136
Adjacent sequences: A078134 A078135 A078136 * A078138 A078139 A078140


KEYWORD

nonn,easy


AUTHOR

Reinhard Zumkeller, Nov 19 2002


EXTENSIONS

Edited by N. J. A. Sloane, Oct 17 2009 at the suggestion of R. J. Mathar.


STATUS

approved



