David Stroup - cp's OEIS frontend

User: David Stroup

David Stroup has authored 2 sequences.

A096142 Let p(0) = 1, p(k) = k-th prime for k >= 1; write 2n = p(i) + p(j) with i <= j and i minimal; sequence gives i.

0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 2, 3, 0, 0, 2, 3, 0, 2, 0, 0, 2, 0, 2, 3, 0, 2, 3, 0, 0, 2, 3, 0, 2, 0, 0, 2, 3, 0, 2, 0, 2, 3, 0, 2, 3, 4, 0, 2, 0, 0, 2, 0, 0, 2, 0, 2, 3, 4, 6, 5, 6, 0, 2, 0, 2, 3, 0, 0, 2, 3, 4, 5, 0, 0, 2, 3, 0, 2, 3, 0, 2, 0, 2, 3, 0, 2, 3, 0, 0, 2, 3, 4, 5, 0, 0, 2, 0

Offset: 1

David Stroup, Jul 23 2004

			a(14)=3, because 28=5+23 (3rd and 9th prime) and 28-1, 28-2, 28-3 are not primes.

a(n) = {tn = 2 * n; ideb = 0; ok = 0; while (! ok, if (ideb == 0, pj = tn -1, pj = tn - prime(ideb)); if (isprime(pj) || (pj == 1), ok = 1, ideb++);); return (ideb);} \\ Michel Marcus, Aug 29 2013

Terms corrected by Michel Marcus, Aug 29 2013

A096139 Number of ways to write 2*n as an ordered sum of two numbers which are prime or 1.

Original entry on oeis.org

1, 3, 3, 4, 3, 4, 5, 4, 6, 6, 5, 8, 5, 4, 8, 6, 7, 8, 5, 6, 10, 8, 7, 12, 8, 6, 12, 6, 7, 14, 7, 10, 12, 6, 10, 14, 11, 10, 14, 10, 9, 18, 9, 8, 20, 8, 9, 14, 8, 12, 18, 12, 11, 18, 14, 14, 22, 12, 11, 24, 7, 10, 20, 8, 14, 20, 11, 10, 18, 16, 15, 22, 11, 10, 26, 10, 16, 22, 11, 16, 20, 12

Offset: 1

David Stroup, Jul 23 2004

A001031(n) = floor((a(n)+1)/2); a(n) mod 2 = A010051(n). - Reinhard Zumkeller, Aug 28 2013

			a(2)=3 because 4=1+3 or 4=2+2 or 4=3+1;
a(3)=3 because 6=1+5 or 6=3+3 or 6=5+1;
a(4)=4 because 8=1+7 or 8=3+5 or 8=5+3 or 8=7+1;
a(5)=3 because 10=3+7 or 10=5+5 or 10=7+3.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Index entries for sequences related to Goldbach conjecture

Cf. A008578, A010051, A001031, A347744.

a096139 n = sum (map a010051 gs') + fromEnum (1 `elem` gs')
   where gs' = map (2 * n -) $ takeWhile (< 2 * n) a008578_list
-- Reinhard Zumkeller, Aug 28 2013

{ a(n) = local(s(n) = if(n==1,1,isprime(n))); sum(i=1,2*n,s(i)*s(2*n-i)); } \\ Christian Krause, Dec 06 2022

Example extended and typo fixed by Reinhard Zumkeller, Aug 28 2013

cp's OEIS Frontend

User: David Stroup

A096142 Let p(0) = 1, p(k) = k-th prime for k >= 1; write 2n = p(i) + p(j) with i <= j and i minimal; sequence gives i.

Views

Author

Keywords

Examples

Programs

PARI

Extensions

A096139 Number of ways to write 2*n as an ordered sum of two numbers which are prime or 1.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Haskell

PARI

Extensions