A328770 Numbers in whose primorial base expansion any digit is at most half of the maximal allowed digit for that position.

0, 2, 6, 8, 12, 14, 30, 32, 36, 38, 42, 44, 60, 62, 66, 68, 72, 74, 90, 92, 96, 98, 102, 104, 210, 212, 216, 218, 222, 224, 240, 242, 246, 248, 252, 254, 270, 272, 276, 278, 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

Offset: 1

Author

Antti Karttunen, Oct 31 2019

Keywords

• nonn
• base

Comments

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.

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

Examples

			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).
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..9072
• Index entries for sequences related to primorial base.

Crossrefs

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

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

Programs

Mathematica

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 *)

PARI

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

Formula

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

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

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