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A333122
Numbers m such that m = prime(k) + prime(k+5) = prime(k+1) + prime(k+4) for some k.
0
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.
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: A228875 A175258 A372991 * A135045 A109321 A349689
KEYWORD
nonn
AUTHOR
Marcin Barylski, Mar 08 2020
STATUS
approved