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 A251925 Prime powers p^k (k>=2) of the form (n^2+1)/2. 0
 25, 841, 28561, 32959081, 1119638521, 1985636569351347658201, 3051519929713402294221039791281, 4689566069222821420312720463003656425961, 183840368926047361112315395593676258316051401, 17020879736268069268391497343746883355223007561030622302744641179601 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The corresponding n are a subsequence of A001333; see example. LINKS Joerg Arndt, Arctan relations for Pi (the author's starting point for this sequence). EXAMPLE The first few terms correspond to 7^2 + 1 = 2 * 5^2 = 2 * 25, 41^2 + 1 = 2 * 29^2 = 2 * 841, 239^2 + 1 = 2 * 13^4 = 2 * 28561, 8119^2 + 1 = 2 * 5741^2 = 2 * 32959081, 47321^2 + 1 = 2 * 33461^2 = 2 * 1119638521, 63018038201^2+1 = 2 * 44560482149^2 = 2 * 1985636569351347658201. PROG (PARI) forstep(n=1, 10^9, 2, t=(n^2+1)/2; if( !isprime(t) && isprimepower(t), print1(t, ", "))); (PARI) /* much more efficient: */ {b(n) = polchebyshev(n, 1, I) / I^n} for(n=1, 10^3, t=(b(n)^2+1)/2; if(!isprime(t)&&isprimepower(t), print1(t, ", "))); CROSSREFS Cf. A027861 (primes of the form (n^2+1)/2), A001333, A008844 (primes and composites with k=2). Sequence in context: A122142 A151557 A008844 * A181892 A274469 A223258 Adjacent sequences:  A251922 A251923 A251924 * A251926 A251927 A251928 KEYWORD nonn AUTHOR Joerg Arndt, Dec 11 2014 STATUS approved

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Last modified April 19 09:12 EDT 2021. Contains 343110 sequences. (Running on oeis4.)