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 A359668 Triangle read by rows. Each number of the triangle is positive and distinct. In row k are the next least k numbers such that the sum of any one number in each of the first k row is a prime number. 0
 2, 3, 5, 6, 12, 24, 18030, 97830, 165690, 392250 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Except for the prime sum of the single number 2 in the first row, all sums are equal to a twin prime. For row k, the k! sums produce as many distinct primes, or, for row k>=2, k!/2 distinct prime twins. Defining this exact triangle from an other angle, e.g. by discovering and describing a regularity in its structure, and/or proving its infinitude, is equivalent to proving the twin prime conjecture. An independent proof of the latter may not prove the infiniteness of this sequence, however. LINKS Table of n, a(n) for n=1..10. EXAMPLE Triangle T(n/k) begins: n/k | 1 2 3 4 -------------------------------------------- 1 | 2; 2 | 3, 5; 3 | 6, 12, 24; 4 | 18030, 97830, 165690, 392250; ... a(5) = 12 because in row three, after a(4), a(5) is the second of the three least values in the row: both a(1) + a(2) + a(5) = 2 + 3 + 12 = 17 and a(1) + a(3) + a(5) = 2 + 5 + 12 = 19 are primes. Below are the prime factors of the elements. These are listed in order of magnitude and without exponents or multiplication symbols, for clarity: 2 3 5 2 3 2 2 3 2 2 2 3 2 3 5 601 2 3 3 5 1087 2 3 3 5 7 263 2 3 5 5 5 523 CROSSREFS Cf. A000040, A001097, A000217, A000142. Sequence in context: A007435 A125877 A118787 * A191783 A358290 A098930 Adjacent sequences: A359665 A359666 A359667 * A359669 A359670 A359671 KEYWORD nonn,tabl,more AUTHOR Tamas Sandor Nagy, Mar 14 2023 EXTENSIONS a(7)-a(10) from Thomas Scheuerle, Mar 14 2023 STATUS approved

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Last modified October 3 13:23 EDT 2023. Contains 365866 sequences. (Running on oeis4.)