A001952 - OEIS (original) (raw)

3, 6, 10, 13, 17, 20, 23, 27, 30, 34, 37, 40, 44, 47, 51, 54, 58, 61, 64, 68, 71, 75, 78, 81, 85, 88, 92, 95, 99, 102, 105, 109, 112, 116, 119, 122, 126, 129, 133, 136, 139, 143, 146, 150, 153, 157, 160, 163, 167, 170, 174, 177, 180, 184, 187, 191, 194, 198

COMMENTS

It appears that the distance between the a(n)-th triangular number and the nearest square is greater than floor(a(n)/2). - Ralf Stephan, Sep 14 2013

REFERENCES

Eric Duchêne, Aviezri S. Fraenkel, Vladimir Gurvich, Nhan Bao Ho, Clark Kimberling, Urban Larsson, Wythoff Visions, Games of No Chance, Vol. 5; MSRI Publications, Vol. 70 (2017), pages 101-153.

R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, Reading, MA, 1990, p. 77.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

L. Carlitz, R. Scoville and V. E. Hoggatt, Jr. Pellian representatives, Fibonacci Quarterly, 10, issue 5, 1972, 449-488.

MATHEMATICA

Array[Floor[#(2+Sqrt[2])]&, 60] (* Harvey P. Dale, Dec 01 2015 *)

PROG

(Haskell)

a001952 = floor . (* (sqrt 2 + 2)) . fromIntegral

(Python)

from sympy import integer_nthroot

def A001952(n): return 2*n+integer_nthroot(2*n**2, 2)[0] # Chai Wah Wu, Mar 16 2021

CROSSREFS

The following sequences are all essentially the same, in the sense that they are simple transformations of each other, with A003151 as the parent: A003151, A001951, A001952, A003152, [A006337](/A006337 "An "eta-sequence": a(n) = floor( (n+1)sqrt(2) ) - floor( nsqrt(2) )."), A080763, A082844 (conjectured), A097509, A159684, A188037, A245219 (conjectured), A276862. - N. J. A. Sloane, Mar 09 2021