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A082176 Professor E.P.B. Umbugio's sequence. 2
0, 0, 206276, 1124101062, 4106026092896, 12565214785548390, 34787981278581970376, 90353184628933414448862, 224610989213093282203310816, 541037084832262355204120965110 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The problem was to prove that 1946 divides every a(n). The proof uses 2141-1770 = 371 = 1863-1492 and 2141-1863= 278 = 1770-1492, gcd(278,371)=1, 278*371=53*1946 and the fact that x-y not 0 divides x^n-y^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) 43-4.

C. A. Pickover, Die Mathematik und das Goettliche, Spektrum Akademischer Verlag, Heidelberg, Berlin, 1999, pp. 56-8,398 (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

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Last modified September 2 22:02 EDT 2014. Contains 246369 sequences.