A179090
Variant of Sylvester's sequence: a(n + 1) = a(n)^2 - a(n) + 1, with a(1) = 14.
Original entry on oeis.org
14, 183, 33307, 1109322943, 1230597390756858307, 1514369938137587813730274566118047943, 2293316309534841541915473293317407057146218304394352680966696226728483307
Offset: 1
- Mohammad K. Azarian, Sylvester's Sequence and the Infinite Egyptian Fraction Decomposition of 1, Problem 958, College Mathematics Journal, Vol. 42, No. 4, September 2011, p. 330. Solution published in Vol. 43, No. 4, September 2012, pp. 340-342.
- Markus Tervooren, Factorizations of Silvester/Euclid sequence 14
A179091
Variant of Sylvester's sequence: a(n + 1) = a(n)^2 - a(n) + 1, with a(1) = 15.
Original entry on oeis.org
15, 211, 44311, 1963420411, 3855019708367988511, 14861176951905611184725545411860008611, 220854580395850552531842289089175529937535309395681309187277137641134140711
Offset: 1
- Mohammad K. Azarian, Sylvester's Sequence and the Infinite Egyptian Fraction Decomposition of 1, Problem 958, College Mathematics Journal, Vol. 42, No. 4, September 2011, p. 330. Solution published in Vol. 43, No. 4, September 2012, pp. 340-342
A179092
Variant of Sylvester's sequence: a(n + 1) = a(n)^2 - a(n) + 1, with a(1) = 16.
Original entry on oeis.org
16, 241, 57841, 3345523441, 11192527090934957041, 125272662681312932108439098957580518641, 15693240015266013784686188640793618219085803766811358216456462217808967968241
Offset: 1
- Mohammad K. Azarian, Sylvester's Sequence and the Infinite Egyptian Fraction Decomposition of 1, Problem 958, College Mathematics Journal, Vol. 42, No. 4, September 2011, p. 330. Solution published in Vol. 43, No. 4, September 2012, pp. 340-342
A179093
Variant of Sylvester's sequence: a(n + 1) = a(n)^2 - a(n) + 1, with a(1) = 17.
Original entry on oeis.org
17, 273, 74257, 5514027793, 30404502496462423057, 924433772057389715967338233131182802193, 854577798920253967214683802805361134256432824758816469437971879296076582807057
Offset: 1
- Mohammad K. Azarian, Sylvester's Sequence and the Infinite Egyptian Fraction Decomposition of 1, Problem 958, College Mathematics Journal, Vol. 42, No. 4, September 2011, p. 330. Solution published in Vol. 43, No. 4, September 2012, pp. 340-342
A179121
Variant of Sylvester's sequence: a(n + 1) = a(n)^2 - a(n) + 1, with a(1) = 18.
Original entry on oeis.org
18, 307, 93943, 8825193307, 77884036897092402943, 6065923203387650816975131277148782658307, 36795424309396699379852983331957135547989414580911143782409880284213748733447943
Offset: 1
- Mohammad K. Azarian, Sylvester's Sequence and the Infinite Egyptian Fraction Decomposition of 1, Problem 958, College Mathematics Journal, Vol. 42, No. 4, September 2011, p. 330. Solution published in Vol. 43, No. 4, September 2012, pp. 340-342
Cf.
A144779,
A144780,
A144781,
A144782,
A144783,
A144784,
A144785,
A179090,
A179091,
A179092,
A179093
A239899
a(0)=2, a(1)=5; thereafter a(n) = product of all preceding terms, minus 1.
Original entry on oeis.org
2, 5, 9, 89, 8009, 64152089, 4115490587216009, 16937262773463574696951813104089
Offset: 0
(9 + 1)*9 - 1 = 89, (89 + 1)*89 - 1 = 8009, (8009 + 1)*8009 - 1 = 64152089. - _Zak Seidov_, Apr 06 2014
-
I:=[2, 5, 9]; [n le 3 select I[n] else Self(n-1)*(Self(n-1)+1)-1: n in [1..10]]; // Vincenzo Librandi, May 22 2014
Comments