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A081463
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.
3
1, 102564, 1012658227848, 105263157894736842, 1014492753623188405797, 1034482758620689655172413793, 102040816326530612244897959183673469387755, 10112359550561797752808988764044943820224719, 1016949152542372881355932203389830508474576271186440677966
OFFSET
1,2
COMMENTS
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
REFERENCES
J. J. Clessa, Micropuzzles, Pan Books, 1983, p. 44 (puzzle 5).
M. J. Halm, More Sequences, Mpossibilities 83, April 2003.
C. A. Pickover, Wonders of Numbers, p. 193.
LINKS
M. J. Halm, Sequences
C. A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," Zentralblatt review
EXAMPLE
a(1) = 102564 because 102564*4 = 410256.
PROG
(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)}
CROSSREFS
Sequence in context: A184567 A034089 A146569 * A321149 A323604 A014884
KEYWORD
nonn,base,fini,full
AUTHOR
Michael Joseph Halm, Apr 20 2003
EXTENSIONS
Edited and missing terms added by Klaus Brockhaus, Apr 22 2003
STATUS
approved