A077287 Unique encountered factors from ( (prime(n)*prime(n+1))^2 + 1 )/2.

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.

Links

Table of n, a(n) for n=2..35.

Chris Nash, PrimeForm - Probable Prime and Classical Primality Testing for 32-bit Windows. [?Broken link]

George F. Woltman, GIMPS - The Great Internet Mersenne Prime Search.

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

Adjacent sequences: A077284 A077285 A077286 * A077288 A077289 A077290

Keyword

nonn

Author

Bill McEachen, Aug 22 2003

Extensions

Edited by Robert G. Wilson v, Sep 27 2003

Status

approved