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A369645
Numbers k for which the difference A051903(k) - A328114(k) reaches a new maximum in range 1..k, where A051903 is the maximal exponent in the prime factorization of n, and A328114 is the maximal digit in the primorial base expansion of n.
2
1, 2, 8, 32, 256, 2560, 30720, 32768, 4194304, 20971520, 58720256, 234881024, 536870912, 1342177280
OFFSET
1,2
EXAMPLE
k factorization max.exp. in primorial max digit diff
base
1 0, 1, 1, -1
2 = 2^1, 1, 10, 1, 0
8 = 2^3, 3, 110, 1, 2
32 = 2^5, 5, 1010, 1, 4
256 = 2^8, 8, 11220, 2, 6
2560 = 2^9 * 5^1, 9, 111120, 2, 7
30720 = 2^11 * 3^1 * 5^1, 11, 1032000, 3, 8
32768 = 2^15, 15, 1120110, 2, 13
4194304 = 2^22, 22, 83876020, 8, 14
20971520 = 2^22 * 5^1, 22, 231462310, 6, 16
58720256 = 2^23 * 7^1, 23, 610501410, 6, 17
234881024 = 2^25 * 7^1, 25, 1141710210, 7, 18
536870912 = 2^29, 29, 296AA71010, 10, 19
1342177280 = 2^28 * 5^1, 28, 6071712310, 7, 21.
On the penultimate row, letter "A" in the primorial base expansion stands for ten (10 in decimal), as 2^29 = 0*prime(0)# + 1*prime(1)# + 0*prime(2)# + 1*prime(3)# + 7*prime(4)# + 10*prime(5)# + 10*prime(6)# + 6*prime(7)# + 9*prime(8)# + 2*prime(9)#, where prime(n)# = A002110(n).
PROG
(PARI)
A051903(n) = if((1==n), 0, vecmax(factor(n)[, 2]));
A328114(n) = { my(s=0, p=2); while(n, s = max(s, (n%p)); n = n\p; p = nextprime(1+p)); (s); };
A350074(n) = (A328114(n) - A051903(n));
m=A350074(1); print1(1, ", "); for(n=2, oo, x=A350074(n); if(x<m, print1(n, ", "); m=x));
CROSSREFS
Positions of records for -A350074(n).
Cf. also A369646, A369647.
After the initial 1, subsequence of A351038, after the two initial terms, subsequence of A350075.
Sequence in context: A048855 A262480 A062797 * A134751 A139014 A063505
KEYWORD
nonn,more
AUTHOR
Antti Karttunen, Feb 01 2024
STATUS
approved