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 A128280 a(n) is the least number not occurring earlier such that a(n)+a(n-1) is prime, a(0) = 0. 19
 0, 2, 1, 4, 3, 8, 5, 6, 7, 10, 9, 14, 15, 16, 13, 18, 11, 12, 17, 20, 21, 22, 19, 24, 23, 30, 29, 32, 27, 26, 33, 28, 25, 34, 37, 36, 31, 40, 39, 44, 35, 38, 41, 42, 47, 50, 51, 46, 43, 54, 49, 48, 53, 56, 45, 52, 55, 58, 69, 62, 65, 66, 61, 70, 57, 74, 63, 64, 67, 60, 71, 68, 59 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Original definition: start with a(1) = 2. See A055265 for start with a(1) = 1. The sequence may well be a rearrangement of natural numbers. Interestingly, subsets of n first terms are permutations of 1..n for n = {2, 4, 8, 10, 18, 22, 24, 56, ...}. E.g. first 56 terms: {2, 1, 4, 3, 8, 5, 6, 7, 10, 9, 14, 15, 16, 13, 18, 11, 12, 17, 20, 21, 22, 19, 24, 23, 30, 29, 32, 27, 26, 33, 28, 25, 34, 37, 36, 31, 40, 39, 44, 35, 38, 41, 42, 47, 50, 51, 46, 43, 54, 49, 48, 53, 56, 45, 52, 55} are a permutation of 1..56. Without altering the definition nor the existing values, one can as well start with a(0) = 0 and get (conjecturally) a permutation of the nonnegative integers. This sequence is in some sense the "arithmetic" analog of the "digital" variant A231433: Here we add subsequent terms, there the digits are concatenated. - M. F. Hasler, Nov 09 2013 The sequence is also a particular case of "among the pairwise sums of any M consecutive terms, N are prime", with M = 2, N = 1. For other M, N see A329333, A329405 ff, A329449 ff and the OEIS Wiki page. - M. F. Hasler, Nov 24 2019 LINKS Lars Blomberg, Table of n, a(n) for n = 0..9999 M. F. Hasler, Prime sums from neighboring terms, OEIS wiki, Nov. 23, 2019. FORMULA a(2n-1) = A055265(2n-1) + 1, a(2n) = A055265(2n) - 1, for all n >= 1. - M. F. Hasler, Feb 11 2020 PROG (PARI) {a=0; u=0; for(n=1, 99, u+=1<

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Last modified April 14 16:38 EDT 2021. Contains 342949 sequences. (Running on oeis4.)