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A077287
Unique encountered factors from ( (prime(n)*prime(n+1))^2 + 1 )/2.
0
113, 613, 5, 24421, 101, 2042221, 13, 41, 60731221, 102975601, 6653, 253102501, 327449641, 17, 14957, 722798221, 37, 35597, 797, 233, 2284271641, 7937, 337, 73, 29, 53, 46414646521, 57358506301, 2521, 89, 89249322541, 61, 281, 56597
OFFSET
2,1
COMMENTS
Write down the prime factors of ( (prime(n)*prime(n+1))^2 + 1 )/2 for n >=2, omitting any that have been observed earlier.
REFERENCES
C. Stanley Ogilvy and John T. Anderson, Excursions in Number Theory. Dover. New York: 1988.
EXAMPLE
Primeform reports 2281 as the factor from ( (P(38321)*P(38322))2+1)/2; this is M17.
MATHEMATICA
PrimeFactors[n_] := Flatten[ Table[ # [[1]], {1}] & /@ FactorInteger[n]]; a = {}; Do[l = PrimeFactors[((Prime[n]*Prime[n + 1])^2 + 1)/2]; If[ Position[a, l[[1]]] == {}, AppendTo[a, l[[1]]]], {n, 2, 127}]; a
PROG
(Gnumeric) cell B2 =pfactor(((A1*A2)^2+1)/2) # supposes the prime list is in col A; Ai, Bi include the cell indices. The output may contain duplicates. - Bill McEachen, Dec 10 2010
CROSSREFS
Sequence in context: A109563 A142024 A300964 * A087294 A152928 A185337
KEYWORD
nonn
AUTHOR
Bill McEachen, Aug 22 2003
EXTENSIONS
Edited by Robert G. Wilson v, Sep 27 2003
STATUS
approved