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A158895
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A list of primes written in order of their first appearance in a table of prime factorizations of 2^k+1, k=1,2,... .
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1
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3, 5, 17, 11, 13, 43, 257, 19, 41, 683, 241, 2731, 29, 113, 331, 65537, 43691, 37, 109, 174763, 61681, 5419, 397, 2113, 2796203, 97, 673, 251, 4051, 53, 157, 1613, 87211, 15790321, 59, 3033169, 61, 1321, 715827883
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OFFSET
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1,1
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COMMENTS
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This sequence has the property that if a(n) appears first in the table as a prime factor of 2^m+1 for some m then a(n)=2*k*m+1 for some k.
When, for some m, 2^m+1 has more than one prime factor appearing in the table for the first time, we adopt the convention of entering them in ascending order. For example, the entries ..., 29, 113, ... both arise from 2^14+1.
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LINKS
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EXAMPLE
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2^1+1=3, 2^2+1=5, 2^3+1=3^2 and 2^4+1=17. Thus a(1)=3, a(2)=5 and a(3)=17, on noting that 2^3+1 contributes no new prime factors.
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MATHEMATICA
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DeleteDuplicates[Flatten[Table[Transpose[FactorInteger[2^k+1]][[1]], {k, 50}]]] (* Harvey P. Dale, Mar 30 2014 *)
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PROG
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(PARI) lista(n)=prs = Set(); for (k=1, n, f = factor(2^k+1); for (i=1, length(f~), onef = f[i, 1]; if (! setsearch(prs, onef), print1(onef, ", "); prs = setunion(prs, Set(onef)); ); ); ); \\ Michel Marcus, Apr 18 2013
(PARI) G=1; for(n=1, 500, g=gcd(f=2^n+1, G); while(g>1, g=gcd(g, f/=g)); f=factor(f)[, 1]; if(#f, for(i=1, #f, print1(f[i]", ")); G*=factorback(f))) \\ Charles R Greathouse IV, Jan 03 2018
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CROSSREFS
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KEYWORD
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nice,nonn
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AUTHOR
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STATUS
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approved
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