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.

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

Table of n, a(n) for n=1..9.

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

Adjacent sequences: A081460 A081461 A081462 * A081464 A081465 A081466

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