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Search: id:A035095
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| A035095 |
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Smallest prime of form k*p(n) + 1, the arithmetical progressions of prime differences. |
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+0
8
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| 3, 7, 11, 29, 23, 53, 103, 191, 47, 59, 311, 149, 83, 173, 283, 107, 709, 367, 269, 569, 293, 317, 167, 179, 389, 607, 619, 643, 1091, 227, 509, 263, 823, 557, 1193, 907, 1571, 653, 2339, 347, 359, 1087, 383, 773, 3547, 797, 2111, 2677, 5449, 2749, 467
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Note that both the terms of this sequence and differences are primes.
This is one possible generalization of "the least prime problem in special arithmetical progressions" when n in the nk+1 form is replaced by n-th prime number.
Smallest numbers m such that largest prime-factor of Phi[m]=p(n), the n-th prime seems to be also prime number and identical to n-th of A035095. See A068211, A068212, A065966: Min[x : A068211(x)=p(n)]=A035095(n); e.g. Phi[a(7)]=Phi[103]=2.3.17 of which 17=p(7) is the largest prime-factor,arising first here.
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..1000
Index entries for sequences related to primes in arithmetic progressions
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FORMULA
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a(n) is the smallest prime such that greatest prime divisor of a(n)-1 is p(n), the n-th prime: a(n)=Min{p, A006530[p-1]=A000040(n)}
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EXAMPLE
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a(8) = 191 because in the p(8)k+1 = 19k+1 sequence 191 is the smallest prime.
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PROGRAM
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(PARI) for(n=1, 80, s=1; while((isprime(s)*s-1)%(prime(n))>0, s++); print1(s, ", "))
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CROSSREFS
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Cf. A034694, A006530, A006093, A035096, A000040, A019434, A058383.
Cf. A068211, A068212, A065966, A000010, A070844-A070858, A061092.
Sequence in context: A103798 A093361 A051202 this_sequence A066674 A125878 A126112
Adjacent sequences: A035092 A035093 A035094 this_sequence A035096 A035097 A035098
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu)
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