A276573 The infinite trunk of least squares beanstalk: The only infinite sequence such that a(0) = 0 and a(n-1) = a(n) - least number of squares (A002828) that sum to a(n).

0, 3, 6, 8, 11, 15, 16, 18, 21, 24, 27, 30, 32, 35, 38, 40, 43, 45, 48, 51, 53, 56, 59, 63, 64, 67, 70, 72, 75, 78, 80, 83, 85, 88, 90, 93, 96, 99, 102, 105, 108, 112, 115, 117, 120, 123, 126, 128, 131, 134, 136, 139, 143, 144, 147, 149, 152, 155, 158, 160, 162, 165, 168, 171, 173, 176, 179, 183, 186, 189, 192, 195

Offset

0,2

Links

Antti Karttunen, Table of n, a(n) for n = 0..10028

Formula

a(n) = A276574(A276572(n)).

Other identities and observations. For all n >= 0:

A260731(a(n)) = n.

a(A260733(n+1)) = A005563(n).

A278517(n) <= a(n) <= A278519(n).

A010873(a(n)) = A278499(n). [Terms reduced modulo 4.]

A010877(a(n)) = A278488(n). [modulo 8.]

A046523(a(n)) = A278497(n). [Least number with the same prime signature.]

A008683(a(n)) = A278513(n).

A065338(a(n)) = A278498(n).

A278509(a(n)) = A278265(n).

A278216(a(n)) = A278516(n). [Number of children the n-th node of the trunk has.]

Prog

(Scheme) (define (A276573 n) (A276574 (A276572 n)))

Crossrefs

Cf. A002828, A005563, A255131, A260731, A260733, A262689, A276572, A276574, A276575 (first differences), A277016 (squares present), A277015 (their square roots), A277888 (primes), A278486 (numbers one more than a prime), A278265, A278487, A278488, A278491 (another subsequence), A278497, A278498, A278499, A278513, A278516, A278517, A278518, A278519, A278521, A278522.

Cf. A277890 & A277891 (number of even and odd terms in each range. The latter seem to be slightly more numerous), A277889.

Positions of nonzero terms in A278515.

Subsequence of A278489, no common terms with A278490.

Cf. also A179016, A259934, A276583, A276613, A276623 for similar constructions.

Sequence in context: A133869 A368642 A356395 * A085197 A164910 A276583

Adjacent sequences: A276570 A276571 A276572 * A276574 A276575 A276576

Keyword

nonn

Author

Antti Karttunen, Sep 07 2016

Extensions

Definition clarified and more identities added to the Formula section by Antti Karttunen, Nov 28 2016

Status

approved