A077214 a(1) = 1. a(n+1) is the smallest number which is greater than a(n), coprime to it and has a different prime signature.

1, 2, 9, 10, 11, 12, 13, 14, 17, 18, 19, 20, 21, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 37, 38, 41, 42, 43, 44, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 77, 78, 79, 80, 81, 82, 83, 84, 85, 88, 89, 90

Offset

1,2

Comments

Subsidiary sequence: First occurrence of a difference n between successive terms. Conjecture : the maximum value of a(k+1) - a(k) = 7 that too occurs only once for k = 2.( i.e. the subsediary sequence has only 7 terms.)

I conjecture that a(n+1)-a(n) is unbounded. The simplest way to get such a gap is to find n divisible by lcm(1,2,...,k) where n+1 has the same prime signature as n. I expect that such numbers exist, although they are likely to be quite large. (Since n-1 lacks small divisors, it is very likely to be in the sequence and so n is also very likely to be in the sequence.) Note that the sequence includes every prime except 3, 5 and 7. - Franklin T. Adams-Watters, Jul 18 2006

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Mathematica

sig[n_] := Sort@FactorInteger[n][[;; , 2]]; f[1] = 2; f[n_] := Module[{sign = sig[n], k = n + 1}, While[! CoprimeQ[n, k] || sig[k] == sign, k++]; k]; NestList[f, 1, 100] (* Amiram Eldar, Dec 29 2020 *)

Crossrefs

Cf. A118914, A124010.

Sequence in context: A131463 A065644 A043065 * A167451 A135782 A281899

Adjacent sequences: A077211 A077212 A077213 * A077215 A077216 A077217

Keyword

nonn

Author

Amarnath Murthy, Nov 02 2002

Extensions

More terms from Franklin T. Adams-Watters, Jul 18 2006

Status

approved