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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

Table of n, a(n) for n=1..10.

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 May 8 19:28 EDT 2021. Contains 343666 sequences. (Running on oeis4.)