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%I #14 Aug 02 2024 17:20:49
%S 1,2,3,4,5,6,7,8,13,14,15,16,17,23,24,25,26,27,33,34,35,36,37,43,44,
%T 45,46,47,53,54,55,56,57,63,64,65,66,67,72,73,74,75,76,77,117,118,124,
%U 125,126,127,128,134,135,136,137,138,144,145,146
%N Numbers with the property that all pairs of consecutive base-9 digits differ by more than 2.
%C Comments from Huen Yeong Kong (cosmology(AT)pacific.net.sg), Sep 19 2008: (Start)
%C Consider the sequence with the first eight terms deleted: 13, 14, 15, 16, 17, 23, 24, 25, 26, 27, 33, 34, 35, 36, 37, 43, 44, 45, 46, 47, 53, 54, 55, ...
%C This sequence extends to infinity starting from the first 5-tuple cluster of 13,14,15,16,17 with higher clusters separated by multiples of 10 intervals. This sequence extended to infinity is completely devoid of twin primes.
%C Example: For n = 10, the sequence generated is: [[13, 14, 15, 16, 17], [23, 24, 25, 26, 27], [33, 34, 35, 36, 37], [43, 44, 45, 46, 47], [53, 54, 55, 56, 57], [63, 64, 65, 66, 67], [73, 74, 75, 76, 77], [83, 84, 85, 86, 87], [93, 94, 95, 96, 97]]
%C Using Macsyma Symbolic Software we can write: makelist( [6+i*10-10-3,6+i*10-10-2,6+i*10-10-1, 6+i*10-10, 6+i*10-10+1], i,2,n); (End)
%t Select[Range[200],Min[Abs[Differences[IntegerDigits[#,9]]]]>2&] (* _Harvey P. Dale_, Aug 02 2024 *)
%Y Cf. A007095.
%K nonn,base
%O 1,2
%A _Clark Kimberling_