A053033 Numbers which are the average of two primes in more ways than any smaller number.

1, 2, 5, 11, 17, 24, 30, 39, 42, 45, 57, 60, 84, 90, 105, 150, 165, 195, 210, 255, 315, 390, 420, 495, 525, 570, 630, 735, 825, 840, 945, 1050, 1155, 1365, 1575, 1785, 1995, 2100, 2205, 2310, 2625, 2730, 3045, 3255, 3465, 3990, 4095

Offset

1,2

Comments

From Ahmad J. Masad, Dec 09 2019: (Start)

Conjecture 1: This sequence is infinite.

Conjecture 2: If this sequence is infinite, then for each prime number p > 2, there exists a minimum sufficiently large number k such that all terms >= k are multiples of p. (End)

Apparently, all terms >= 90 are multiples of 15. - Hugo Pfoertner, Dec 09 2019

Positions of records in A045917. - Sean A. Irvine, Dec 04 2021

Links

Giovanni Resta, Table of n, a(n) for n = 1..266 (terms < 10^7)

Example

a(1) = 1: average of 0 pairs of primes;
a(2) = 2: average of 1 pair of primes (2,2);
a(3) = 5: average of 2 pairs of primes (3,7), (5,5);
a(4) = 11: average of 3 pairs of primes (3,19), (5,17), (11,11);
a(5) = 17: average of 4 pairs of primes (3,31), (5,29), (11,23), (17,17).

Maple

(for n>0): printlevel := -1:maxx := 0:for j from 2 to 1000 do count := 0; for k from 0 to j-2 do if (isprime(j-k) and isprime(j+k)) then count := count+1 fi od; if count>maxx then print(j, count); maxx := count fi od;

Crossrefs

Cf. A002375, A045917.

Sequence in context: A086319 A220813 A217303 * A136244 A115057 A228344

Adjacent sequences: A053030 A053031 A053032 * A053034 A053035 A053036

Keyword

nonn

Author

Len Smiley, Feb 23 2000

Extensions

More terms from James A. Sellers, Feb 25 2000

Status

approved