A003508 - OEIS

A003508

a(1) = 1; for n>1, a(n) = a(n-1) + 1 + sum of distinct prime factors of a(n-1) that are < a(n-1).
(Formerly M0580)

1, 2, 3, 4, 7, 8, 11, 12, 18, 24, 30, 41, 42, 55, 72, 78, 97, 98, 108, 114, 139, 140, 155, 192, 198, 215, 264, 281, 282, 335, 408, 431, 432, 438, 517, 576, 582, 685, 828, 857, 858, 888, 931, 958, 1440, 1451, 1452, 1469, 1596, 1628, 1679, 1776, 1819, 1944

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

R. K. Guy reports, Apr 14 2005: In Math. Mag. 48 (1975) 301 one finds "C. W. Trigg, C. C. Oursler and R. Cormier & J. L. Selfridge have sent calculations on Problem 886 [Nov 1973] for which we had received only partial results [Jan 1975]. Cormier and Selfridge sent the following results: There appear to be five sequences beginning with integers less than 1000 which do not merge. These sequences were carried out to 10^8 or more." The five sequences are A003508, A105210-A105213.

This suggests that there may be infinitely many different (non-merging) sequences obtained by choosing different starting values.

All terms of these five sequences are distinct up to least 10^30. - T. D. Noe, Oct 19 2007

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

T. D. Noe, Table of n, a(n) for n=1..2000

Doug Engel, Problem 886, Math. Mag., 48 (1975), 57-58.

EXAMPLE

a(6)=8, so a(7) = 8 + 1 + 2 = 11.

MATHEMATICA

a[1] = 1; a[n_] := a[n] = a[n - 1] + 1 + Plus @@ Select[ Flatten[ Table[ #[[1]], {1}] & /@ FactorInteger[ a[n - 1]]], # < a[n - 1] &]; Table[ a[n], {n, 54}] (* Robert G. Wilson v, Apr 13 2005 *)

nxt[n_]:=n+1+Total[Select[Transpose[FactorInteger[n]][[1]], #<n&]]; NestList[ nxt, 1, 60] (* Harvey P. Dale, Jul 19 2015 *)

PROG

(Haskell)

a003508 n = a003508_list !! (n-1)

a003508_list = 1 : map

(\x -> x + 1 + sum (takeWhile (< x) $ a027748_row x)) a003508_list

-- Reinhard Zumkeller, Jan 15 2015

CROSSREFS

Cf. A096460, A105221, A105233.

Cf. A027748, A105210, A105211, A105212, A105213.

Sequence in context: A284937 A271441 A328421 * A225229 A239389 A256219

Adjacent sequences: A003505 A003506 A003507 * A003509 A003510 A003511