A016067 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

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

FORMULA

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

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