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A152913
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Primes of the form n^4 + (n+1)^4.
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17
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17, 97, 337, 881, 3697, 10657, 16561, 49297, 66977, 89041, 149057, 847601, 988417, 1146097, 1972097, 2522257, 2836961, 3553777, 3959297, 4398577, 5385761, 7166897, 11073217, 17653681, 32530177, 41532497, 44048497, 55272097, 61627201
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OFFSET
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1,1
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COMMENTS
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Sequence is disjoint to A005385: If n^4 + (n+1)^4 is a prime p, then (p-1)/2 = n^4 + 2*n^3 + 3*n^2 + 2*n. (p-1)/2 = 8 for n = 1 and (p-1)/2 is divisible by n for n > 1. In each case, (p-1)/2 is not prime.
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LINKS
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EXAMPLE
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For n=3, n^4 + (n+1)^4 = 337 is prime and (337-1)/2 = 168 = 3*56 is not prime.
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MATHEMATICA
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Select[Table[n^4+(n+1)^4, {n, 0, 700}], PrimeQ]
Select[Total/@Partition[Range[100]^4, 2, 1], PrimeQ] (* Harvey P. Dale, Sep 29 2023 *)
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PROG
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(Magma) [ a: n in [1..80] | IsPrime(a) where a is n^4+(n+1)^4 ];
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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