A158877 -id:A158877 - cp's OEIS frontend

A159774 Least number m, written in base n, such that m/2 is obtained merely by shifting the leftmost digit of m to the right end, and 2m by shifting the rightmost digit of m to the left end, digits defined in base n.

1012, 102, 102342, 1031345242, 103524563142, 1042, 10467842, 105263157894736842, 316, 10631694842

Offset: 3

William A. Hoffman III (whoff(AT)robill.com), Apr 21 2009

10(b2) and 31(b5) do not both halve and double by rotations. No 2-digit answer can meet the description, so the sequence begins with a base 3 value.

			1042(b8)/2 = 421(b8) and 1042(b8)*2 = 2104(b8)
316 (base 11) = 380 (base 10), 163 (base 11) = 190 (base 10), 631 (base 11) = 760 (base 10).

W. A. Hoffman III, Algorithm to compute terms.

Cf. A092697, A097717, A094224, A094676, A158877.

See A147514 for these numbers written in base 10.

Offset corrected by N. J. A. Sloane, Apr 23 2009
a(11) corrected. To indicate that terms from base n=13 on need digits larger than 9, keywords fini, full added. - Ray Chandler and R. J. Mathar, Apr 23 2009
Edited by Ray Chandler, May 02 2009

A087502 Smallest positive integer which when written in base n is doubled when the last digit is put first.

Original entry on oeis.org

32, 18, 8, 10993850, 2129428800, 21, 5064320, 105263157894736842, 40, 64609423538, 5712, 65, 58774271029236501660840264682112, 67650, 96, 833, 586081355679130611935159482937228562988190880, 133

Offset: 3

Pontus von Brömssen, Sep 10 2003

a(n) is the smallest integer of the form x*(n^d-1)/(2n-1) for integer x and d, where 1 < x < n and d > 1. x is the last digit and d is the number of digits of a(n) in base n. - Pontus von Brömssen, Jan 06 2019

			a(10) = 105263157894736842 because 2*105263157894736842 = 210526315789473684 and no smaller number has this property. (Leading zeros are not allowed, otherwise 2*052631578947368421 = 105263157894736842 would be a smaller solution.)

Pontus von Brömssen, Table of n, a(n) for n = 3..221

See A158877 for these numbers written in base n. Cf. A023094, A034089, A081463, A087502.

A087502 := proc(n) local d,a; d := 1; a := n; while a>=n do d := d+1; a := denom((2^d-1)/(2*n-1)); od; return(max(2,a)*(n^d-1)/(2*n-1)); end proc;

cp's OEIS Frontend

A159774 Least number m, written in base n, such that m/2 is obtained merely by shifting the leftmost digit of m to the right end, and 2m by shifting the rightmost digit of m to the left end, digits defined in base n.

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