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A103808
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Primes from merging of 6 successive digits in decimal expansion of the Golden Ratio; (1+sqrt(5))/2.
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30
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339887, 458683, 638117, 628189, 902449, 418939, 189391, 386891, 235369, 693179, 607667, 595939, 613199, 171169, 631361, 497587, 864449, 987433, 544877, 647809, 217057, 705751, 427621, 410117, 666599, 979873, 731761, 874807, 530567, 228911
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OFFSET
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1,1
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COMMENTS
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Leading zeros are not permitted, so each term is 6 digits in length. - Harvey P. Dale, Oct 23 2011
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LINKS
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Mohammad K. Azarian, Problem 123, Missouri Journal of Mathematical Sciences, Vol. 10, No. 3, Fall 1998, p. 176. Solution published in Vol. 12, No. 1, Winter 2000, pp. 61-62.
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MATHEMATICA
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With[{len=6}, FromDigits/@Select[Partition[RealDigits[GoldenRatio, 10, 1000][[1]], len, 1], PrimeQ[FromDigits[#]] &&IntegerLength[ FromDigits[#]] ==len&]] (* Harvey P. Dale, Oct 23 2011 *)
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PROG
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(PARI) A103808(n, x=(sqrt(5)+1)/2, m=6, silent=0)={m=10^m; for(k=1, default(realprecision), (isprime(p=x\.1^k%m)&&p*10>m)||next; silent||print1(p", "); n--||return(p))} \\ The optional arguments can be used to produce other sequences of this series (cf. Crossrefs). Use, e.g., \p999 to set precision to 999 digits. - M. F. Hasler, Nov 01 2014
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CROSSREFS
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See also, for e: A104843, A104844, A104845, A104846, A104847, A104848, A104849, A104850, A104851; for Pi: A104824, A104825, A104826, A198170, A198171, A198172, A198173, A198175; for sqrt(2): A198161, A198162, A198163, A198164, A198165, A198166, A198167, A198168, A198169; for the Euler-Mascheroni constant gamma: A198776, A198777, A198778, A198779, A198780, A198781, A198782, A198783, A198784 and A104944.
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KEYWORD
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nonn,base
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AUTHOR
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Andrew G. West (WestA(AT)wlu.edu), Mar 29 2005
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EXTENSIONS
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STATUS
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approved
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