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A131992
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a(n) = 1 + prime(n) + prime(n)^2 + prime(n)^3 + prime(n)^4.
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11
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31, 121, 781, 2801, 16105, 30941, 88741, 137561, 292561, 732541, 954305, 1926221, 2896405, 3500201, 4985761, 8042221, 12326281, 14076605, 20456441, 25774705, 28792661, 39449441, 48037081, 63455221, 89451461, 105101005, 113654321
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OFFSET
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1,1
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COMMENTS
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Giovanni Resta has found that 28792661 is the first Sophie Germain prime of this form (and actually of the form p = (n^m-1)/(n-1) for any p-1 > n, m > 1). - M. F. Hasler, Mar 03 2020
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REFERENCES
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Victor Thébault, Curiosités arithmétiques, Mathesis 62 (1953), pp. 120-129.
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LINKS
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FORMULA
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a(n) = (prime(n)^5 - 1)/(prime(n) - 1) = A053699(prime(n)). (This is also meant by the 2nd formula.) - M. F. Hasler, Mar 03 2020
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EXAMPLE
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a(1) = 31 because prime(1) = 2 and 1 + 2 + 2^2 + 2^3 + 2^4 = 1 + 2 + 4 + 8 + 16 = 31.
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MATHEMATICA
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Table[Sum[Prime[n]^k, {k, 0, 4}], {n, 30}] (* Alonso del Arte, May 24 2015 *)
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PROG
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CROSSREFS
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Equals A053699 restricted to prime indices. Subsequence of primes is A190527.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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