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A208295 a(n)*(a(n)+1) + A002973(n)^2 = A005098(n), n>=1. 2
0, 1, 0, 2, 0, 2, 3, 2, 1, 2, 4, 0, 1, 3, 5, 3, 5, 6, 4, 3, 0, 7, 6, 7, 0, 6, 4, 2, 8, 6, 5, 4, 2, 8, 3, 8, 9, 0, 1, 7, 8, 3, 10, 9, 2, 5, 10, 9, 6, 0, 11, 2, 8, 9, 12, 6, 12, 11, 0, 2, 7, 13, 4, 9, 12 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

See the Jon Perry comment on A005098. The (even) promic number a(n)*(a(n)+1) (see A002378) when subtracted from A005098(n) (the n-th value k such that 4*k+1 is prime) leaves a square, namely A002973(n)^2. E.g., n=4: 7 - 2*3 = 1^1. n=5: 9 - 0 = 3^2.

2*a(n)+1 = A002972(n), n>=1. E.g., n=4: 2*2+1=5.

LINKS

Table of n, a(n) for n=1..65.

FORMULA

a(n) = (sqrt(4*(k(n) - m(n)^2)+1)-1)/2, n>=1, with k(n) := A005098(n) (4*k(n)+1 is the prime A002144(n)) and m(n):= A002973(n).

a(n) = (A002972(n)-1)/2, n>=1.

CROSSREFS

Cf. A005098, A002144, A002972, A002973, A002378.

Sequence in context: A104513 A305610 A220455 * A285721 A214292 A212184

Adjacent sequences:  A208292 A208293 A208294 * A208296 A208297 A208298

KEYWORD

nonn

AUTHOR

Wolfdieter Lang, Mar 01 2012

STATUS

approved

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Last modified October 22 15:45 EDT 2018. Contains 316490 sequences. (Running on oeis4.)