A081463 - OEIS

%I #12 Dec 18 2016 01:22:32

%S 1,102564,1012658227848,105263157894736842,1014492753623188405797,

%T 1034482758620689655172413793,

%U 102040816326530612244897959183673469387755,10112359550561797752808988764044943820224719,1016949152542372881355932203389830508474576271186440677966

%N Numbers which when multiplied by their final digit have products with same digital sequence except that last is first. Numbers obtained by concatenating a term any number of times with itself also have the defining property and are omitted.

%C The final digit determines the number by an obvious algorithm (see PARI program), hence the sequence has exactly nine terms (for final digit 1, ..., 9), self-concatenations being excluded. - _Klaus Brockhaus_, Apr 24 2003

%D J. J. Clessa, Micropuzzles, Pan Books, 1983, p. 44 (puzzle 5).

%D M. J. Halm, More Sequences, Mpossibilities 83, April 2003.

%D C. A. Pickover, Wonders of Numbers, p. 193.

%H M. J. Halm, <a href="http://untilheaven.tripod.com/id112.htm">Sequences</a>

%H C. A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," <a href="http://www.zentralblatt-math.org/zmath/en/search/?q=an:0983.00008&amp;format=complete">Zentralblatt review</a>

%e a(1) = 102564 because 102564*4 = 410256.

%o (PARI) {f(digit)=local(v,m,k,c,s); v=""; m=0; k=digit; c=0; while(m!=digit,v=concat(k,v); m=digit*k+c; s=divrem(m,10); c=s[1]; k=s[2]); eval(v)}

%K nonn,base,fini,full

%O 1,2

%A _Michael Joseph Halm_, Apr 20 2003

%E Edited and missing terms added by _Klaus Brockhaus_, Apr 22 2003