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Search: id:A141830
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| A141830 |
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Primes p such that 1|p, 2|(p+1), 3|(p+2), 4|(p+3),...,(q-p)|(q-1), where q is the prime immediately after p. |
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3
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| 2, 3, 5, 11, 13, 17, 29, 37, 41, 59, 61, 71, 97, 101, 107, 109, 137, 149, 179, 191, 193, 197, 227, 229, 239, 269, 277, 281, 311, 313, 347, 349, 397, 419, 431, 457, 461, 521, 541, 569, 599, 601, 613, 617, 641, 659, 673, 757, 769, 809, 821, 827, 853, 857, 877
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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This sequence also gives the primes p such that every positive integer k <= q-p divides p-1, where q is the prime immediately after p.
Number of terms less than 10^k: 3, 13, 57, 338, 2020, 13569, 98365, 736332, 5729411, ..., . Compare these to A006880. - Robert G. Wilson v, Aug 01 2008
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LINKS
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Robert G. Wilson v, Table of n, for n = 1..13569.
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MAPLE
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isA141830 := proc(p) local q, d ; if isprime(p) then q := nextprime(p) ; for d from 1 to q-p do if (p+d-1) mod d <> 0 then RETURN(false) ; fi; od: RETURN(true) ; else false; fi; end: for i from 1 to 300 do p := ithprime(i) ; if isA141830(p) then printf("%d, ", p) ; fi; od: [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 08 2008]
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MATHEMATICA
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fQ[n_] := Block[{p = n, q = NextPrime@ n}, Union[IntegerQ /@ (Range[p, q - 1]/Range[q - p])][[1]]]; Select[ Prime@ Range@ 151, fQ@# &] (* RGWv *)
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CROSSREFS
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Cf. A141829, A141831.
Sequence in context: A127046 A127051 A127045 this_sequence A127048 A139053 A038615
Adjacent sequences: A141827 A141828 A141829 this_sequence A141831 A141832 A141833
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KEYWORD
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nonn
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AUTHOR
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Leroy Quet (q1qq2qqq3qqqq(AT)yahoo.com), Jul 09 2008
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com) and R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 08 2008
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