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A002972 a(n) is the odd member of {x,y}, where x^2+y^2 is the n-th prime of the form 4i+1.
(Formerly M2221)
16
1, 3, 1, 5, 1, 5, 7, 5, 3, 5, 9, 1, 3, 7, 11, 7, 11, 13, 9, 7, 1, 15, 13, 15, 1, 13, 9, 5, 17, 13, 11, 9, 5, 17, 7, 17, 19, 1, 3, 15, 17, 7, 21, 19, 5, 11, 21, 19, 13, 1, 23, 5, 17, 19, 25, 13, 25, 23, 1, 5, 15, 27, 9, 19, 25, 17, 11, 5, 25, 27, 23, 29, 29, 25, 23, 19, 29, 13, 31, 31 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n)^2 + 4*A002973(n)^2 = A002144(n); A002331(n+1)=MIN(a(n),2*A002973(n)) and A002330(n+1)=MAX(a(n),2*A002973(n)). [Reinhard Zumkeller, Feb 16 2010]

It appears that the terms in this sequence are the absolute values of the terms in A046730. [Gerry Myerson, Dec 02 2010]

(a(n)-1)/2 = A208295(n), n>=1. [Wolfdieter Lang, Mar 03 2012]

a(A267858(k)) == 1 (mod 4), k >= 1. - Wolfdieter Lang, Feb 18 2016

REFERENCES

E. Kogbetliantz and A. Krikorian, Handbook of First Complex Prime Numbers, Gordon and Breach, NY, 1971, p. 243.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

T. D. Noe, Table of n, a(n) for n=1..1000

S. R. Finch, Powers of Euler's q-Series, arXiv:math/0701251 [math.NT], 2007.

E. Kogbetliantz and A. Krikorian, Handbook of First Complex Prime Numbers, Gordon and Breach, NY, 1971. [Annotated scans of a few pages]

FORMULA

a(n) = MIN(A173330(n), A002144(n) - A173330(n)). [Reinhard Zumkeller, Feb 16 2010]

EXAMPLE

The 2nd prime of the form 4i+1 is 13=2^2+3^2, so a(2)=3.

MATHEMATICA

pmax = 1000; odd[p_] := Module[{k, m}, 2m+1 /. ToRules[Reduce[k>0 && m >= 0 && (2k)^2 + (2m+1)^2 == p, {k, m}, Integers]]]; For[n=1; p=5, p<pmax, p = NextPrime[p], If[Mod[p, 4] == 1, a[n] = odd[p]; Print["a(", n, ") = ", a[n]]; n++]]; Array[a, n-1] (* Jean-François Alcover, Feb 26 2016 *)

CROSSREFS

Cf. A002144, A002973, A261858.

Sequence in context: A348161 A334194 A046730 * A324896 A029652 A238952

Adjacent sequences:  A002969 A002970 A002971 * A002973 A002974 A002975

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Better description from Jud McCranie, Mar 05 2003

STATUS

approved

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Last modified November 30 06:28 EST 2021. Contains 349419 sequences. (Running on oeis4.)