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 A283814 Irregular triangle read by rows in which n-th row lists the numbers m such that 2*prime(m) can be represented  as the sum of two primes in exactly n ways. 1
 1, 2, 3, 4, 8, 5, 6, 11, 7, 9, 10, 18, 12, 13, 14, 15, 22, 16, 17, 19, 21, 23, 24, 25, 27, 29, 30, 34, 38, 46, 20, 28, 42, 26, 31, 32, 36, 37, 40, 50, 41, 43, 58, 33, 35, 39, 45, 47, 52, 53, 59, 44, 48, 49, 65, 51, 61, 62, 55, 57, 60, 66, 67, 70, 85, 54, 56, 63, 68, 72, 73, 75, 77, 79, 64, 76, 78, 80, 81, 83 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS From b116619.txt it seems that the sequence is correct at least for first 677 terms (first 100 rows of triangle). But as it is usual in number theory better consider this sequence as conjectured. Lengths of first 100 rows of triangle (see a283814.txt): {2,3,3,4,5,5,8,3,7,3,8,4,3,7,8,1,10,7,6,9,3,7,6,3,4,7,13,4,6,7,7,9,7,8,8,3,8,8,5,5,5,11,5,10,3,6,8,10,5,8,5,9,6,9,6,7,10,6,6,6,8,5,7,12,11,6,8,6,9,4,12,6,8,5,5,5,11,10,13,7,7,10,9,7,4,9,7,5,4,8,7,6,10,7,6,10,6,10,6,6}. LINKS Zak Seidov, First 100 rows of the triangle. EXAMPLE 3rd row is {5,6,11} because only the 5th, 6th and 11th primes can be represented as the sum of 2 primes in exactly 3 ways: n=3: 2*prime(5) = 2*11 = 22 = 3 + 19 = 5 + 17 = 11 + 11, 2*prime(6) = 2*13 = 26 = 3 + 23 = 7 + 19 = 13 + 13, 2*prime(11) = 2*31 = 62 = 3 + 59 = 7 + 19 = 19 + 43 = 31 + 31. MATHEMATICA A116619=Table[Count[PrimeQ[2*Prime[n]-Prime[Range[n]]], True], {n, 1000}]; Flatten[Position[A116619, #]& /@ Range[100]] CROSSREFS Cf. A116619 (number of ways of representing 2*prime(n) as the sum of two primes). Sequence in context: A175060 A138773 A132989 * A114881 A246273 A082319 Adjacent sequences:  A283811 A283812 A283813 * A283815 A283816 A283817 KEYWORD nonn,tabf AUTHOR Zak Seidov, Mar 17 2017 STATUS approved

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Last modified April 18 12:42 EDT 2019. Contains 322209 sequences. (Running on oeis4.)