A016067 Consider all ways of writing a number as p+2m^2 where p is 1 or a prime and m >= 0; sequence gives numbers that are expressible in at least 2 more ways than any smaller number.
139, 181, 619, 2341, 3331, 4189, 4801, 5911, 6319, 8251, 9751, 11311, 12739, 13051, 15889, 20641, 21349, 22741, 23659, 24079, 32191, 33631, 39961, 42871, 45769, 56131, 57511, 65341, 71839, 80149, 90919, 95989, 99181, 105271, 119131, 130651, 157261, 167359
Offset: 1
Keywords
Links
- Donovan Johnson, Table of n, a(n) for n = 1..245 (terms <= 2*10^9)
- G. H. Hardy and J. E. Littlewood, Some problems of 'Partitio numerorum'; III: On the expression of a number as a sum of primes, Acta Math., Vol. 44, No. 1 (1923), pp. 1-70.
- L. Hodges, A lesser-known Goldbach conjecture, Math. Mag., 66 (1993), 45-47.
- M. Stern, Sur une assertion de Goldbach relative aux nombres impairs, Nouvelles Annales Math., 15 (1856) pp. 23-24.
- Index entries for sequences related to Goldbach conjecture
Programs
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Haskell
import Data.List (findIndices) a016067 n = a016067_list !! (n-1) a016067_list = (map (+ 1) $ findIndices (> 1) $ zipWith (-) (tail rs) rs where rs = scanl max 0 a046920_list -- Reinhard Zumkeller, Aug 26 2013, Apr 03 2013
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PARI
/* finds first 80 terms */ mx=6023671; v=vector(mx); p=vector(414391); p[1]=1; pr=1; for(j=2, 414391, pr=nextprime(pr+1); p[j]=pr); for(m=0, 1735, m2=2*m^2; for(j=1, 414391, s=m2+p[j]; if(s<=mx, v[s]++, next(2)))); c=0; n=0; for(j=1, mx, if(v[j]>c, if(v[j]>=c+2, n++; write("b016067.txt", n " " j)); c=v[j])) /* Donovan Johnson, Aug 24 2013 */
Formula
Extensions
Better description and more terms from Jud McCranie, Jun 16 2000
Invalid first term removed by Donovan Johnson, Aug 24 2013