A333122 Numbers m such that m = prime(k) + prime(k+5) = prime(k+1) + prime(k+4) for some k.

24, 30, 60, 84, 102, 210, 234, 288, 330, 378, 420, 426, 496, 528, 588, 594, 624, 690, 1050, 1156, 1200, 1218, 1302, 1336, 1410, 1470, 1484, 1638, 1650, 1680, 1686, 1716, 1734, 1740, 1746, 1788, 1848, 1908, 1918, 1930, 2052, 2154, 2226, 2364, 2410, 2580, 2892, 2934, 3168, 3524, 4080

Offset

1,1

Comments

Terms are always even because all primes used in this sequence are odd.

Conjecture: this sequence is infinite.

Links

Table of n, a(n) for n=1..51.

Example

a(1)=24 because prime(3)+prime(8)=prime(4)+prime(7)=5+19=7+17.

Mathematica

(#[[1]] + #[[6]]) & /@ Select[ Partition[ Prime@ Range@ 320, 6, 1], #[[1]] + #[[6]] == #[[2]] + #[[5]] &] (* Giovanni Resta, Mar 08 2020 *)

Prog

(Python)
from sympy import nextprime
A333122_list, plist = [], [2, 3, 5, 7, 11, 13]
while len(A333122_list) < 10000:
    m = plist[0]+plist[5]
    if m == plist[1]+plist[4]:
        A333122_list.append(m)
    plist = plist[1:] + [nextprime(plist[-1])] # Chai Wah Wu, Mar 30 2020

Crossrefs

Cf. A022889 (the prime(k) primes), A105093 (similar sequence).

Sequence in context: A334790 A228875 A175258 * A135045 A109321 A349689

Adjacent sequences: A333119 A333120 A333121 * A333123 A333124 A333125

Keyword

nonn

Author

Marcin Barylski, Mar 08 2020

Status

approved