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a(n) is the least number whose sum of digits in primorial base equals n.
5

%I #12 Nov 14 2024 08:21:48

%S 0,1,3,5,11,17,23,29,59,89,119,149,179,209,419,629,839,1049,1259,1469,

%T 1679,1889,2099,2309,4619,6929,9239,11549,13859,16169,18479,20789,

%U 23099,25409,27719,30029,60059,90089,120119,150149,180179,210209,240239,270269

%N a(n) is the least number whose sum of digits in primorial base equals n.

%C Equivalently, this sequence gives positions of records in A276150.

%H Rémy Sigrist, <a href="/A343048/b343048.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>

%F A276150(a(n)) = n.

%F a(n) = A060735(n)-1. - _Antti Karttunen_, Nov 14 2024

%e The first terms, alongside their primorial base representation, are:

%e n a(n) prim(a(n))

%e -- ---- ----------

%e 0 0 0

%e 1 1 1

%e 2 3 11

%e 3 5 21

%e 4 11 121

%e 5 17 221

%e 6 23 321

%e 7 29 421

%e 8 59 1421

%e 9 89 2421

%e 10 119 3421

%e 11 149 4421

%e 12 179 5421

%e 13 209 6421

%e 14 419 16421

%e 15 629 26421

%o (PARI) a(n) = my (v=0, pp=1); forprime (p=2, oo, if (n==0, return (v), my (d=min(p-1, n)); n-=d; v+=d*pp; pp*=p))

%Y Cf. A200748, A276150.

%Y One less than A060735.

%Y Cf. also A372559.

%K nonn,base

%O 0,3

%A _Rémy Sigrist_, Apr 05 2021