The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A334185 Let m = d*q + r be the Euclidean division of m by d. The terms m of this sequence satisfy that r, q, d are consecutive positive integer terms in a geometric progression with a common integer ratio. 5
 9, 28, 34, 65, 75, 110, 126, 132, 205, 217, 246, 258, 294, 344, 399, 436, 502, 513, 520, 579, 657, 680, 730, 810, 866, 978, 979, 1001, 1028, 1128, 1164, 1330, 1332, 1365, 1374, 1582, 1605, 1729, 1736, 1815, 1947, 2004, 2050, 2064, 2196, 2198, 2310, 2329, 2610, 2710 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Inspired by the problem 141 of Project Euler (see the link). If b is the common ratio, then b is an integer >= 2. So, when b >= 2 and r >= 1, q=r*b, d=r*b^2, then every m = r * (1+r*b^3) is a term, and the division becomes: r*(1+r*b^3) = (r*b^2) * (r*b) + r. The integers (r, r*b, r*b^2) are in geometric progression. When (r= 1 and b >= 2; so, when r = 1, A001093(n) for n>1 are terms (see 1st example). LINKS Wikipedia, Euclidean division EXAMPLE a(2) = 28 = 9*3 + 1 with (1,3,9) and ratio = 3; a(5) = 75 = 12*6 + 3 with (3,6,12) and ratio = 2; a(12) = 258 = 32*8 + 2 with (2,8,32) and ratio = 4; a(42) = 2004 = 100*20 + 4 with (r=4, q=20, d=100) but also 2004 = 20*100 + 4 with (r=4, d'=20, q'=100) both with ratio = 5: 2004 | 100             2004 |  20      ------                 ------    4 |  20                4 | 100 MATHEMATICA Select[Range, Length @ Solve[r * (1 + r*b^3) == # && r >=1 && b >= 2, {r, b}, Integers] > 0 &] (* Amiram Eldar, Apr 18 2020 *) PROG (PARI) isok(m) = {for (d=1, m, if (m % d, q = m\d; r = m % d; if (!(d % q) && (d/q == q/r), return (1)); ); ); } \\ Michel Marcus, Apr 19 2020 CROSSREFS Cf. A334186 (similar with b is an irreductible fraction). Subsequence: A001093 \ {0, 1, 2} (for r = 1). Sequence in context: A044999 A155473 A127629 * A267686 A024670 A141805 Adjacent sequences:  A334182 A334183 A334184 * A334186 A334187 A334188 KEYWORD nonn AUTHOR Bernard Schott, Apr 18 2020 EXTENSIONS Name improved by Michel Marcus, Apr 19 2020 More terms from Michel Marcus, Apr 19 2020 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 17 08:24 EDT 2021. Contains 343064 sequences. (Running on oeis4.)