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A328770
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Numbers in whose primorial base expansion any digit is at most half of the maximal allowed digit for that position.
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6
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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
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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FORMULA
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Because doubling these numbers in primorial base does not generate any carries, it follows that:
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EXAMPLE
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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).
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MATHEMATICA
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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 *)
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PROG
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(PARI) isA328770(n) = { my(p=2); while(n, if((n%p)>((p-1)/2), return(0)); n = n\p; p = nextprime(1+p)); (1); };
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CROSSREFS
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Subsequence of A276154 (because of Bertrand's postulate).
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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