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

Author

Marcin Barylski, Mar 08 2020

Keywords

• nonn

Comments

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

Conjecture: this sequence is infinite.

Examples

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

Crossrefs

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

Programs

Mathematica

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

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