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A272063 a(n) = largest k such that A004431(n) +/- k are both positive squares. 0
4, 6, 12, 8, 16, 24, 10, 20, 30, 12, 24, 40, 36, 14, 48, 28, 42, 60, 56, 32, 48, 70, 64, 18, 84, 80, 54, 72, 96, 20, 40, 90, 60, 112, 80, 108, 22, 100, 126, 120, 88, 144, 110, 48, 140, 72, 132, 96, 160, 120, 154, 52, 78, 144, 180 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

There can be more than one value of k such that A004431(n) +/- k are both positive squares; i.e., when there are multiple ways to express A004431(n) as the sum of positive squares. These are the terms which appear more than once in A055096. For example A004431(19) = 65 = {(1^2 + 8^2), (4^2 + 7^2)}: 65 +/- 16 = {7^2, 9^2} and 65 +/- 56 = {3^2, 11^2}. So a(19) = 56 rather than 16.

Similar to A270835; differences occur for n<56 at n = {19,25,38,39,42,51}; i.e., terms A004431(n) which appear more than once in A055096.

Sequence contains every even number >=4 and no odd numbers.

LINKS

Table of n, a(n) for n=1..55.

FORMULA

a(n) = A004431(n)-1 when A004431(n) = k^2 + (k+1)^2 == A001844(k), k>=1.

EXAMPLE

a(11)=24 because A004431(11) = 40; 40+24 = 8^2 and 40-24 = 4^2.

CROSSREFS

Cf. A001844, A004431, A055096, A270835.

Sequence in context: A278252 A274298 A270835 * A152678 A110758 A189765

Adjacent sequences:  A272060 A272061 A272062 * A272064 A272065 A272066

KEYWORD

nonn

AUTHOR

Bob Selcoe, Apr 19 2016

STATUS

approved

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Last modified July 2 09:32 EDT 2022. Contains 354999 sequences. (Running on oeis4.)