A357614 Lexicographically earliest infinite sequence of distinct positive integers such that a(n+1) is the least k != j, for which gcd(k, j) > 1, where j = a(n) + prime(n).
1, 6, 3, 2, 12, 46, 118, 5, 4, 9, 8, 13, 10, 15, 14, 122, 7, 11, 16, 166, 18, 21, 20, 206, 25, 22, 24, 254, 19, 26, 278, 27, 28, 30, 39, 32, 33, 34, 394, 17, 35, 36, 31, 37, 23, 38, 42, 44, 45, 40, 538, 48, 41, 47, 50, 614, 1754, 49, 52, 56, 674, 29, 54, 57, 58
Offset: 1
Keywords
Examples
a(1)=1; 1 + prime(1)=3, so a(2) = 6, the smallest unused number sharing a divisor with 3.
Links
- Michael De Vlieger, Table of n, a(n) for n = 1..10000
- Michael De Vlieger, Log log scatterplot of a(n), n = 1..2^14, labeling maxima in red and local minima in blue, highlighting primes in green and other prime powers in gold.
Programs
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Mathematica
nn = 65; c[] = False; u = 2; a[1] = j = 1; c[1] = True; Do[m = j + Prime[n - 1]; If[PrimeQ[m], k = 2; While[c[k m], k++]; k *= m, k = u; While[Or[c[k], k == m, CoprimeQ[k, m]], k++]]; Set[{a[n], c[k], j}, {k, True, k}]; If[k == u, While[c[u], u++]], {n, 2, nn}]; Array[a, nn] (* _Michael De Vlieger, Oct 06 2022 *)
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