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

1,2

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.

Links

Antti Karttunen, Table of n, a(n) for n = 1..9072

Index entries for sequences related to primorial base.

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.

Example

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).

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 *)

Prog

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

Crossrefs

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

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

Sequence in context: A153880 A120227 A276154 * A138626 A178406 A189515

Adjacent sequences: A328767 A328768 A328769 * A328771 A328772 A328773

Keyword

nonn,base

Author

Antti Karttunen, Oct 31 2019

Status

approved