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A071331
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Numbers n such that there is no decomposition of n into a sum of two prime powers.
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5
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1, 149, 331, 373, 509, 701, 757, 809, 877, 907, 959, 997, 1019, 1087, 1199, 1207, 1211, 1243, 1259, 1271, 1477, 1529, 1541, 1549, 1589, 1597, 1619, 1657, 1719, 1759, 1777, 1783, 1807, 1829, 1859, 1867, 1927, 1969, 1973, 2171, 2231
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Luca & Stanica show that this sequence contains infinitely many Fibonacci numbers. In particular, there is some N such that for all n > N, Fibonacci(1807873 + 3543120*n) is in this sequence. [Charles R Greathouse IV, Jul 06 2011]
Chen shows that there are five consecutive odd numbers M-8, M-6, M-4, M-2, M, for which all are members of the sequence. Such M may be large; Chen shows that it is less than 2^(2^253000). In fact, there exists an arithmetic progression of such M, and thus they have positive density. [Charles R Greathouse IV, Jul 06 2011]
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
Florian Luca and Pantelimon Stanica, Fibonacci numbers that are not sums of two prime powers, Proceedings of the American Mathematical Society 133 (2005), pp. 1887-1890.
Yong-Gao Chen, Five consecutive positive odd numbers, none of which can be expressed as a sum of two prime powers, Mathematics of Computation 74 (2005), pp. 1025-1031.
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PROG
| (PARI) isprimepower(n)=ispower(n, , &n); isprime(n)||n==1;
isA071331(n)=forprime(p=2, n\2, if(isprimepower(n-p), return(0))); forprime(p=2, sqrtint(n\2), for(e=1, log(n\2)\log(p), if(isprimepower(n-p^e), return(0)))); !isprimepower(n-1)
\\ Charles R Greathouse IV, Jul 06 2011
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CROSSREFS
| A071330(a(n))=0. Cf. A000961.
Cf. A109829, A014092.
Sequence in context: A105843 A131573 A146137 * A095842 A115231 A142359
Adjacent sequences: A071328 A071329 A071330 * A071332 A071333 A071334
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KEYWORD
| nonn,nice
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 19 2002
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