A191614 The lexicographically earliest sequence such that a(n) - a(n-1) is the largest proper divisor of a(n).

1, 2, 3, 6, 7, 14, 21, 42, 43, 86, 129, 258, 301, 602, 903, 1806, 1849, 3698, 5547, 11094, 12943, 25886, 38829, 77658, 77659, 155318, 232977, 465954, 543613, 1087226, 1630839, 3261678, 3339337, 6678674, 10018011, 20036022, 23375359, 46750718, 70126077, 140252154

Offset: 1

Author

Jaroslav Krizek, Jun 09 2011

Keywords

• nonn

Comments

In contrast, A000079(n) is the lexicographically *largest* sequence such that a(n) - a(n-1) is the largest proper divisor of a(n).

Sequence is infinite because A060681 is surjective.

Crossrefs

Cf. A105017, A064097, A175125, A060681.

Programs

Maple

A191614 := proc(n) option remember; if n = 1 then 1; else for m from 1 do if m-A032742(m) = procname(n-1) then return m; end if; end do: end if; end proc: # R. J. Mathar, Jun 13 2011

PARI

p=0; for (v=1, 140252154, if (v%(v-p)==0 && (p==0 || (d=divisors(v))[#d-1]==v-p), print1 (p=v ", "))) \\ Rémy Sigrist, Apr 24 2021

Formula

a(n) is the smallest number m such that m - A032742(m) = a(n-1), n > 1.

Extensions

More terms from Rémy Sigrist, Apr 24 2021