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A328622
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In primorial base representation of n, multiply by 2 all other digits except the least significant, and reduce each such product modulo prime(k) (to get the new digit), where k > 1 is the position of the digit, then convert back to decimal.
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9
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0, 1, 4, 5, 2, 3, 12, 13, 16, 17, 14, 15, 24, 25, 28, 29, 26, 27, 6, 7, 10, 11, 8, 9, 18, 19, 22, 23, 20, 21, 60, 61, 64, 65, 62, 63, 72, 73, 76, 77, 74, 75, 84, 85, 88, 89, 86, 87, 66, 67, 70, 71, 68, 69, 78, 79, 82, 83, 80, 81, 120, 121, 124, 125, 122, 123, 132, 133, 136, 137, 134, 135, 144, 145, 148, 149, 146, 147, 126, 127, 130, 131
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OFFSET
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0,3
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LINKS
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FORMULA
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EXAMPLE
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In primorial base (A049345) 199 is written as "6301" because 6*A002110(3) + 3*A002110(2) + 0*A002110(1) + 1*A002110(0) = 6*30 + 3*6 + 0*2 + 1*1 = 199. Multiplying each digit except the least significant by 2, and then reducing them modulo the corresponding prime leaves us with 2*6 mod 7, 2*3 mod 5, 2*0 mod 3, (with the least significant 1 staying the same), so we get "5101", which is the primorial base expansion of 157, thus a(199) = 157.
For 157, the new "doubled and reduced" expansion is 2*5 mod 7, 2*1 mod 5, 2*0 mod 3 and the trailing 1 stays intact, so we get "3201", which is the primorial base expansion of 103, thus a(157) = 103.
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PROG
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(PARI)
A002110(n) = prod(i=1, n, prime(i));
A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*A002110(primepi(f[k, 1])-1)); };
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A328618(n) = { my(f = factor(n), m, q); for(k=1, #f~, q = (f[k, 2]\f[k, 1]); m = (f[k, 2]%f[k, 1]); if(m&&(f[k, 1]!=2), f[k, 2] = q*f[k, 1] + ((2*f[k, 2])%f[k, 1]))); factorback(f); };
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CROSSREFS
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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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