The On-Line Encyclopedia of Integer Sequences (OEIS)

A055047 revision #40

A055047

Numbers of the form 9^i*(3*j+1).

1, 4, 7, 9, 10, 13, 16, 19, 22, 25, 28, 31, 34, 36, 37, 40, 43, 46, 49, 52, 55, 58, 61, 63, 64, 67, 70, 73, 76, 79, 81, 82, 85, 88, 90, 91, 94, 97, 100, 103, 106, 109, 112, 115, 117, 118, 121, 124, 127, 130, 133, 136, 139, 142, 144, 145, 148, 151

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OFFSET

1,2

COMMENTS

The numbers not of the form 2x^2+3y^2+3z^2.

Also values of n such that numbers of the form x^2+n*y^2 for some integers x, y cannot have prime factor of 3 raised to an odd power. - V. Raman, Dec 18 2013

Numbers whose squarefree part is congruent to 1 modulo 3. - Peter Munn, May 17 2020

REFERENCES

L. J. Mordell, A new Waring's problem with squares of linear forms, Quart. J. Math., 1 (1930), 276-288 (see p. 283).

LINKS

Table of n, a(n) for n=1..58.

FORMULA

a(n) = 8n/3 + O(log n). - Charles R Greathouse IV, Dec 19 2013

a(n) = A055041(n)/3. - Peter Munn, May 17 2020

PROG

(PARI) is(n)=n/=9^valuation(n, 9); n%3==1 \\ Charles R Greathouse IV and V. Raman, Dec 19 2013

CROSSREFS

Intersection of A007417 and A189715.