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

Author

Antti Karttunen, Sep 07 2016

Keywords

• nonn

Links

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

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.

Programs

Scheme

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

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.]

Extensions

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