A328770 - OEIS

%I #18 Mar 13 2024 01:50:37

%S 0,2,6,8,12,14,30,32,36,38,42,44,60,62,66,68,72,74,90,92,96,98,102,

%T 104,210,212,216,218,222,224,240,242,246,248,252,254,270,272,276,278,

%U 282,284,300,302,306,308,312,314,420,422,426,428,432,434,450,452,456,458,462,464,480,482,486,488,492,494,510,512,516,518,522

%N Numbers in whose primorial base expansion any digit is at most half of the maximal allowed digit for that position.

%C Equally, numbers in whose primorial base expansion there are no digits more than ((prime(k)-1)/2), where prime(k) is the modulus for the digit position k = 1 + maximal allowed digit for that position.

%C Differs from A276154, for example, this sequence does not contain term 120.

%H Antti Karttunen, <a href="/A328770/b328770.txt">Table of n, a(n) for n = 1..9072</a>

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

%F a(n) = A328849(n)/2.

%F Because doubling these numbers in primorial base does not generate any carries, it follows that:

%F A276086(a(n)+a(n)) = A276086(a(n)) * A276086(a(n)) = A328834(n)^2.

%e 2 is included, as in the primorial base (A049345) it is written as "10", thus 2 is included in the sequence as the maximal value that can occur in the second rightmost digit (in the primorial base representation) is 2 (as in "20" = 4 or "21" = 5 for example).

%t q[n_] := Module[{k = n, p = 2, s = {}, r}, While[{k, r} = QuotientRemainder[k, p]; k != 0 || r != 0, AppendTo[s, r]; p = NextPrime[p]]; AllTrue[s/(Prime[Range[1, Length[s]]] - 1), # <= 1/2 &]]; Select[Range[0, 600], q] (* _Amiram Eldar_, Mar 13 2024 *)

%o (PARI) isA328770(n) = { my(p=2); while(n, if((n%p)>((p-1)/2), return(0)); n = n\p; p = nextprime(1+p)); (1); };

%Y Subsequence of A276154 (because of Bertrand's postulate).

%Y Cf. A002110, A049345, A276086, A328834, A328849.

%K nonn,base

%O 1,2

%A _Antti Karttunen_, Oct 31 2019