A147514 Least number m, written in base 10, 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.

32, 18, 3472, 10993850, 2129428800, 546, 5064320, 105263157894736842, 380, 64609423538, 11424, 1673230, 58774271029236501660840264682112, 67650, 122181448512, 1666, 586081355679130611935159482937228562988190880, 210051282051282, 13571630704729343835960800

Offset

3,1

Comments

Serves as an extension to A159774, which misses proper representation for solutions beyond base 12.

Algorithm: write m in base b with LSB d_0, k middle digits d_m, and MSB digit d_e as m=d_0+d_m*b+d_e*b^(k+1).

Demand m/2 = d_e+d_0*b_d_m*b^2 and 2*m=d_m+d_e*b^k+d_0*b^(k+1). Mix these to obtain m*(2b-1)=2*d_e*(b^(k+2)-1).

Loop over (outer loop) k=0,1,2... and (inner loop d_e=0.. b-1 to obtain integer m to be checked against the condition.

Links

Table of n, a(n) for n=3..21.

Crossrefs

Cf. A159774.

Sequence in context: A023094 A087502 A070628 * A291155 A070620 A070627

Adjacent sequences: A147511 A147512 A147513 * A147515 A147516 A147517

Keyword

base,nonn

Author

Ray Chandler and R. J. Mathar, Apr 23 2009

Status

approved