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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. 7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Max{A046920(k): k <= a(n)} + 1 < A046920(a(n)). - Reinhard Zumkeller, Aug 26 2013, Apr 03 2013

REFERENCES

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., 44 (1922) pp. 1-70.

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

LINKS

Donovan Johnson, Table of n, a(n) for n = 1..245 (terms <= 2*10^9)

L. Hodges, A lesser-known Goldbach conjecture, Math. Mag., 66 (1993), 45-47.

Index entries for sequences related to Goldbach conjecture

PROG

(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

(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 */

CROSSREFS

Cf. A007697, A046920.

Sequence in context: A209618 A031928 A095649 * A142524 A108383 A027867

Adjacent sequences:  A016064 A016065 A016066 * A016068 A016069 A016070

KEYWORD

nonn

AUTHOR

Robert G. Wilson v

EXTENSIONS

Better description and more terms from Jud McCranie, Jun 16, 2000

Invalid first term removed by Donovan Johnson, Aug 24 2013

STATUS

approved

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Last modified June 17 19:10 EDT 2019. Contains 324198 sequences. (Running on oeis4.)