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A007697 Smallest odd number expressible in at least n ways as p+2*m^2 where p is 1 or a prime and m >= 0.
(Formerly M2292)
7

%I M2292

%S 1,3,13,19,55,61,139,139,181,181,391,439,559,619,619,829,859,1069,

%T 1081,1459,1489,1609,1741,1951,2029,2341,2341,3331,3331,3331,3961,

%U 4189,4189,4261,4801,4801,5911,5911,5911,6319,6319,6319,8251,8251,8251,8251,8251

%N Smallest odd number expressible in at least n ways as p+2*m^2 where p is 1 or a prime and m >= 0.

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

%D Moritz A. Stern, Sur un assertion de Goldbach relative aux nombres impairs, Nouvelles Annales Math. 15 (1856), 23-24.

%H Donovan Johnson, <a href="/A007697/b007697.txt">Table of n, a(n) for n = 1..10000</a>

%H G. H. Hardy and J. E. Littlewood, <a href="https://doi.org/10.1007/BF02403921">Some problems of 'Partitio numerorum'; III: On the expression of a number as a sum of primes</a>, Acta Math., Vol. 44, No. 1 (1923), pp. 1-70.

%H L. Hodges, <a href="https://www.jstor.org/stable/2690477">A lesser-known Goldbach conjecture</a>, Math. Mag., 66 (1993), 45-47.

%H <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>

%t max = 9000; sp = Outer[Plus, Prepend[Prime /@ Range[PrimePi[max]], 1], 2*Range[0, Ceiling[Sqrt[max/2]]]^2] // Flatten // Sort // Split;

%t a[1] = 3; a[n_] := (sel = Select[sp, Length[#] >= n &];

%t If[sel == {}, {}, sel[[1, 1]]]); a /@ Range[47]

%t (* _Jean-Fran├žois Alcover_, Apr 29 2011 *)

%o (Haskell)

%o import Data.List (findIndex)

%o import Data.Maybe (fromJust)

%o a007697 n = 2 * (fromJust $ findIndex (>= n) a046921_list) + 1

%o -- _Reinhard Zumkeller_, Apr 03 2013

%Y Cf. A016067, A046921.

%K nonn,nice,easy,changed

%O 1,2

%A _N. J. A. Sloane_.

%E Stern and Hardy-Littlewood references suggested by _Ctibor O. Zizka_, Apr 14 2008

%E Edited by _N. J. A. Sloane_, May 15 2008 at the suggestion of _R. J. Mathar_

%E a(1) changed to 1 at the suggestion of _Donovan Johnson_. - _N. J. A. Sloane_, May 10 2011

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Last modified July 30 15:29 EDT 2021. Contains 346359 sequences. (Running on oeis4.)