

A082176


Professor E.P.B. Umbugio's sequence.


2



0, 0, 206276, 1124101062, 4106026092896, 12565214785548390, 34787981278581970376, 90353184628933414448862, 224610989213093282203310816, 541037084832262355204120965110
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OFFSET

0,3


COMMENTS

The problem was to prove that 1946 divides every a(n). The proof uses 21411770 = 371 = 18631492 and 21411863= 278 = 17701492, gcd(278,371)=1, 278*371=53*1946 and the fact that xy not 0 divides x^ny^n for n>=0. See the Starke reference. The primes which divide every a(n) are 2,7,53,139. Note the historical dates other than 2141 in the formula. This AMM problem was proposed in 1946 (with a reference to April 1).


REFERENCES

H. E. G. P., Elementary problem No. E716, Professor Umbugio's Prediction; Solution by E. P. Starke, American Math. Monthly 54 (1947) 434.
C. A. Pickover, Die Mathematik und das Goettliche, Spektrum Akademischer Verlag, Heidelberg, Berlin, 1999, pp. 568,398 (English: The Loom of God, Plenum, 1997).


LINKS

Table of n, a(n) for n=0..9.


FORMULA

a(n)= 1492^n  1770^n  1863^n + 2141^n.


CROSSREFS

Cf. A082177, A082178.
Sequence in context: A234061 A234060 A115946 * A178285 A101701 A092011
Adjacent sequences: A082173 A082174 A082175 * A082177 A082178 A082179


KEYWORD

nonn,easy


AUTHOR

Wolfdieter Lang, Apr 25 2003


STATUS

approved



