Joshua Michael McAteer - cp's OEIS frontend

User: Joshua Michael McAteer

Joshua Michael McAteer has authored 2 sequences.

A326953 a(n) = A001222(A028906(n)).

1, 1, 1, 1, 1, 1, 1, 2, 5, 3, 1, 1, 1, 1, 2, 1, 2, 1, 3, 1, 1, 1, 1, 3, 1, 3, 3, 3, 4, 1, 2, 1, 2, 3, 1, 2, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 3, 3, 2, 3, 3, 1, 1, 5, 4, 3, 2, 3, 1, 7, 3, 3, 1, 1, 2, 1, 1, 1, 2, 2, 1, 2, 1, 2, 3, 1, 2, 3, 4, 1, 1, 1, 1, 2, 1, 5, 3, 1, 1, 3, 2, 3, 1, 3, 3, 4, 1, 4, 1

Offset: 1

Joshua Michael McAteer, Aug 06 2019

Multiplicity of prime divisors of n, where n is a number composed of the reverse sorted digits of a prime number.

Conjecture: the sum of the first n terms of A326953 (largest to smallest sorting) is >= the sum of the first n terms of A326952 (smallest to largest sorting). This is true for the first 9592 terms.

			The 28th prime number is 107. The reverse sorted digits are 710. The factorization of 710 is 2, 5, 71, therefore the 28th term in this sequence is 3.

Joshua Michael McAteer, Table of n, a(n) for n = 1..9592

Cf. A001222 (bigomega), A028906, A326952 (for ascending sorted version).

nmax= 100;
p = primes(nmax);
lp = length(p);
lfac = zeros(1, lp);
for i = 1:lp
digp=str2double(regexp(num2str(p(i)), '\d', 'match'));
ldigp = flip(sort(digp));
l=length(digp);
conv = 10.^flip(0:(l-1));
lnum = sum(conv.*ldigp);
lfac(i) = numel(factor(lnum));
end

A326952 a(n) = A001222(A028905(n)).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 1, 4, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 4, 1, 1, 1, 2, 2, 1, 1, 1, 5, 1, 1, 1, 1, 1, 3, 3, 1, 3, 1, 1, 1, 7, 3, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 3, 1, 1, 2, 2, 1, 3, 2, 2, 1, 4, 1, 1, 2, 2, 1, 1, 2, 1, 1, 2, 1, 3, 2, 2

Offset: 1

Joshua Michael McAteer, Aug 06 2019

Multiplicity of prime divisors of n, where n is a number composed of the sorted digits of a prime number.

Conjecture: the sum of the first n terms of A326952 (smallest to largest sorting) is <= the sum of the first n terms of A326953 (largest to smallest sorting). This is true for the first 9592 terms.

			The 13th prime number is 41. Sorting the digits gives 14. 14 has 2 factors, 2 and 7. The 13th term of this sequence is 2.

Joshua Michael McAteer, Table of n, a(n) for n = 1..9592

Cf. A001222 (bigomega), A028905, A326953 (for reverse sorting).

nmax= 100;
p = primes(nmax);
lp = length(p);
sfac = zeros(1,lp);
for i = 1:lp
digp=str2double(regexp(num2str(p(i)),'\d','match'));
sdigp = sort(digp);
l=length(digp);
conv = 10.^flip(0:(l-1));
snum = sum(conv.*sdigp);
sfac(i) = numel(factor(snum));
end

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User: Joshua Michael McAteer

A326953 a(n) = A001222(A028906(n)).

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