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A304868 Numbers x satisfying x == 1 (mod 4) or x == 14, 26, 30 (mod 32). 1
1, 5, 9, 13, 14, 17, 21, 25, 26, 29, 30, 33, 37, 41, 45, 46, 49, 53, 57, 58, 61, 62, 65, 69, 73, 77, 78, 81, 85, 89, 90, 93, 94, 97, 101, 105, 109, 110, 113, 117, 121, 122, 125, 126, 129, 133, 137, 141, 142, 145, 149, 153, 154, 157, 158, 161, 165, 169, 173, 174, 177 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The sum of two distinct terms of this sequence is never a square.

Sequence has density 11/32, the maximal density that can be attained with such a sequence.

REFERENCES

J. P. Massias, Sur les suites dont les sommes des termes 2 à 2 ne sont pas des carrés, Publications du département de mathématiques de Limoges, 1982.

LINKS

Colin Barker, Table of n, a(n) for n = 1..1000

J. C. Lagarias, A. M. Odlyzko, J. B. Shearer, On the density of sequences of integers the sum of no two of which is a square. I. Arithmetic progressions, Journal of Combinatorial Theory. Series A, 33 (1982), pp. 167-185.

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,0,1,-1).

FORMULA

From Colin Barker, May 20 2018: (Start)

G.f.: x*(1 + 4*x + 4*x^2 + 4*x^3 + x^4 + 3*x^5 + 4*x^6 + 4*x^7 + x^8 + 3*x^9 + x^10 + 2*x^11) / ((1 - x)^2*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^9 + x^10)).

a(n) = a(n-1) + a(n-11) - a(n-12) for n>12.

(End)

PROG

(PARI) isok(n) = ((n%4)==1) || ((n%32)==14) || ((n%32)==26) || ((n%32)==30);

(PARI) Vec(x*(1 + 4*x + 4*x^2 + 4*x^3 + x^4 + 3*x^5 + 4*x^6 + 4*x^7 + x^8 + 3*x^9 + x^10 + 2*x^11) / ((1 - x)^2*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^9 + x^10)) + O(x^40)) \\ Colin Barker, May 20 2018

CROSSREFS

Cf. A016777 (another such sequence), A210380.

Sequence in context: A241987 A189464 A130333 * A080579 A325274 A303264

Adjacent sequences:  A304865 A304866 A304867 * A304869 A304870 A304871

KEYWORD

nonn,easy

AUTHOR

Michel Marcus, May 20 2018

STATUS

approved

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Last modified October 6 04:36 EDT 2022. Contains 357261 sequences. (Running on oeis4.)