A276582 -id:A276582 - cp's OEIS frontend

A276583 The infinite trunk of greedy squares beanstalk: The only infinite sequence such that a(n-1) = a(n) - number of squares that sum to a(n) with greedy algorithm (A053610).

0, 3, 6, 8, 11, 15, 18, 21, 24, 27, 32, 35, 38, 43, 48, 51, 56, 59, 63, 66, 71, 74, 78, 80, 83, 88, 91, 95, 99, 102, 107, 110, 114, 117, 120, 123, 128, 131, 135, 138, 143, 146, 151, 154, 158, 161, 164, 168, 171, 176, 179, 183, 186, 192, 195, 198, 203, 206, 210, 213, 219, 224, 227, 232, 235, 239, 242, 248, 251, 255

Offset: 0

Antti Karttunen, Sep 07 2016

nonn

Antti Karttunen, Table of n, a(n) for n = 0..10095

Cf. A053610, A260740, A276582, A276584, A276585 (first differences).

Cf. also A179016, A259934, A276573, A276613, A276623 for similar constructions.

(define (A276583 n) (A276584 (A276582 n)))

a(n) = A276584(A276582(n)).

A276581 After a(0)=0, each n occurs A261224(n) times.

Original entry on oeis.org

0, 1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 17, 17, 17, 18

Offset: 0

Antti Karttunen, Sep 07 2016

nonn

Auxiliary function for computing A276582 & A276583.

Antti Karttunen, Table of n, a(n) for n = 0..9996

Cf. A261223, A261224, A276582, A276583.

Table[Table[n, {-1 + Length@ NestWhileList[# - Block[{m = #, c = 1}, While[a = (# - Floor[Sqrt@ #]^2) &@ m; a != 0, c++; m = a]; c] &, ((n + 1)^2) - 1, # != n^2 - 1 &]}], {n, 0, 18}] // Flatten (* Michael De Vlieger, Sep 08 2016 *)

(define (A276581 n) (let loop ((k 0)) (if (>= (A261223 (+ 1 k)) n) k (loop (+ 1 k)))))

A276584 The infinite trunk of greedy squares beanstalk with reversed subsections.

Original entry on oeis.org

0, 3, 8, 6, 15, 11, 24, 21, 18, 35, 32, 27, 48, 43, 38, 63, 59, 56, 51, 80, 78, 74, 71, 66, 99, 95, 91, 88, 83, 120, 117, 114, 110, 107, 102, 143, 138, 135, 131, 128, 123, 168, 164, 161, 158, 154, 151, 146, 195, 192, 186, 183, 179, 176, 171, 224, 219, 213, 210, 206, 203, 198, 255, 251, 248, 242, 239, 235, 232, 227

Offset: 0

Antti Karttunen, Sep 07 2016 and Sep 09 2016

nonn

Antti Karttunen, Table of n, a(n) for n = 0..9996

Cf. A000196, A000290, A010052, A053610, A260740, A276582, A276583.

(definec (A276584 n) (cond ((zero? n) n) ((= 1 n) 3) (else (let ((maybe_next (A260740 (A276584 (- n 1))))) (if (zero? (A010052 (+ 1 maybe_next))) maybe_next (+ -1 (A000290 (+ 2 (A000196 (+ 1 maybe_next))))))))))

a(0) = 0; a(1) = 3; for n > 1, if A260740(a(n-1))+1 is not a square, then a(n) = A260740(a(n-1)), otherwise a(n) = A000290(2+A000196(A260740(a(n-1)))) - 1.

cp's OEIS Frontend

A276583 The infinite trunk of greedy squares beanstalk: The only infinite sequence such that a(n-1) = a(n) - number of squares that sum to a(n) with greedy algorithm (A053610).

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A276581 After a(0)=0, each n occurs A261224(n) times.

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A276584 The infinite trunk of greedy squares beanstalk with reversed subsections.

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