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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 (list; graph; refs; listen; history; text; internal format)
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 A067952

Adjacent sequences:  A333119 A333120 A333121 * A333123 A333124 A333125

KEYWORD

nonn

AUTHOR

Marcin Barylski, Mar 08 2020

STATUS

approved

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Last modified April 20 01:20 EDT 2021. Contains 343117 sequences. (Running on oeis4.)