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

Author

Michael Joseph Halm, Apr 20 2003

Keywords

• nonn
• base
• fini
• full

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

Examples

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

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

Programs

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)}

Extensions

Edited and missing terms added by Klaus Brockhaus, Apr 22 2003