%I #15 Apr 10 2021 04:12:50

%S 1176470588235294,2352941176470588,3529411764705882,4705882352941176,

%T 5882352941176470,11764705882352941176470588235294,

%U 23529411764705882352941176470588,35294117647058823529411764705882,47058823529411764705882352941176,58823529411764705882352941176470

%N Numbers k such that when the first digit of k is shifted to the end the result is 3*k/2.

%C The problem of finding the least number in this sequence was suggested by the Polish-British mathematician and historian Jacob Bronowski (1908-1974).

%C Anderson (1988) credited the problem to the British mathematician John Edensor Littlewood (1885-1977). The solution to the problem was given in 1955 by the British mathematician Dudley Ernest Littlewood (1903-1979), a student of J. E. Littlewood (but they were not related).

%D Jacob Bronowski, New Statesman and Nation, Vol. 39, Dec. 24, 1949, p. 761.

%D Dan Pedoe, The Gentle Art of Mathematics, Macmillan, 1960, p. 11.

%H Amiram Eldar, <a href="/A337922/b337922.txt">Table of n, a(n) for n = 1..310</a>

%H Oliver D. Anderson, <a href="https://doi.org/10.1093/teamat/7.3.144">On Littlewood's Little Puzzle</a>, Teaching Mathematics and its Applications: An International Journal of the IMA, Vol. 7, No. 3 (1988), pp. 144-146.

%H J. H. Clarke, <a href="https://www.jstor.org/stable/3608209">Note 2298. A Digital Puzzle</a>, The Mathematical Gazette, Vol. 36, No. 318 (1952), p. 276.

%H Keith Devlin, <a href="https://doi.org/10.1007/978-1-349-07936-0">Micro-Maths, Mathematical problems and theorems to consider and solve on a computer</a>, Macmillan, 1984, pp. 38-39.

%H D. E. Littlewood, <a href="https://www.jstor.org/stable/3611102">Note 2494. On Note 2298: a digital puzzle</a>, The Mathematical Gazette, Vol. 39, No. 327 (1955), p. 58.

%H Joseph S. Madachy, <a href="https://www.fq.math.ca/Scanned/6-6/madachy.pdf">Recreational Mathematics</a>, The Fibonacci Quarterly, Vo. 6, No. 6 (1968), pp. 385-398. See page 389.

%H Math Stackexchange, <a href="https://math.stackexchange.com/questions/1301639/finding-the-dr-bronowskis-number">Finding the Dr. Bronowski's number</a>, 2015.

%H Sidney Penner, <a href="http://www.jstor.org/stable/2310848">Problem E 1530</a>, Elementary Problems and Solutions, The American Mathematical Monthly, Vol. 69, No. 7 (1962), p. 667; J. W. Ellis and others, <a href="http://www.jstor.org/stable/2311879">Placing the First Digit Last, Solution to Problem E 1530</a>, ibid., Vol. 70, No. 4 (1963), pp. 441-442.

%H D. G. Rogers, <a href="http://www.jstor.org/stable/27821833">Jacob Bronowski (1908-1974) The Mathematical Gazette and retrodigitisation</a>, The Mathematical Gazette, Vol. 92, No. 525 (2008), pp. 476-479; <a href="http://maths.mq.edu.au/wp-content/uploads/2015/03/MG2008JB.pdf">alternative link</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Transposable_integer">Transposable integer</a>.

%F The decimal digits of the first 5 terms are the periodic parts of the decimal expansions of 2/17, 4/17, 6/17, 8/17 and 10/17. The next terms are all the concatenations of each of these terms with itself an integral number of times (Anderson, 1988).

%e 1176470588235294 is a term since 1764705882352941 = 3*1176470588235294/2.

%t concat[n_, m_] := NestList[FromDigits[Join[{#}, IntegerDigits[n]]] &, n, m]; s = Range[2, 10, 2]*(10^16 - 1)/17; Union @ Flatten[concat[#, 2] & /@ s]

%Y Cf. A061242, A166320, A258663.

%K nonn,base

%O 1,1

%A _Amiram Eldar_, Jan 29 2021