A032986 Numbers with the property that all pairs of consecutive base-9 digits differ by more than 2.

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, 45, 46, 47, 53, 54, 55, 56, 57, 63, 64, 65, 66, 67, 72, 73, 74, 75, 76, 77, 117, 118, 124, 125, 126, 127, 128, 134, 135, 136, 137, 138, 144, 145, 146

Offset

1,2

Comments

Comments from Huen Yeong Kong (cosmology(AT)pacific.net.sg), Sep 19 2008: (Start)

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, ...

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.

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]]

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)

Links

Table of n, a(n) for n=1..59.

Mathematica

Select[Range[200], Min[Abs[Differences[IntegerDigits[#, 9]]]]>2&] (* Harvey P. Dale, Aug 02 2024 *)

Crossrefs

Cf. A007095.

Sequence in context: A165306 A254116 A254115 * A032977 A133245 A200374

Adjacent sequences: A032983 A032984 A032985 * A032987 A032988 A032989

Keyword

nonn,base

Author

Clark Kimberling

Status

approved