A249342 -id:A249342 - cp's OEIS frontend

A249337 a(1) = 1, a(2) = 2; for n>2, a(n) = number of values k in range 1 .. n-1 such that {sum of prime indices in the prime factorization of a(k)} = {sum of prime indices in the prime factorization of a(n-1)}, both counted with multiplicity.

1, 2, 1, 2, 2, 3, 1, 3, 2, 4, 3, 4, 5, 1, 4, 6, 2, 5, 3, 7, 1, 5, 4, 8, 5, 6, 7, 2, 6, 8, 9, 3, 9, 4, 10, 5, 10, 6, 11, 1, 6, 12, 7, 8, 13, 1, 7, 9, 10, 11, 2, 7, 12, 13, 2, 8, 14, 3, 11, 4, 12, 14, 5, 15, 6, 16, 15, 7, 16, 17, 1, 8, 17, 2, 9, 18, 8, 18, 9, 19, 1, 9, 20, 10, 21, 3, 13, 4, 14, 11, 12, 22, 5, 19, 2, 10, 23, 1

Offset: 1

Antti Karttunen, Oct 25 2014

nonn

Antti Karttunen, Table of n, a(n) for n = 1..12580

Cf. A056239, A249072 (sum of prime indices of n-th term), A249341 (positions of ones), A249342 (positions of the first occurrences of each noncomposite).

Cf. also A249336 (a similar sequence with a slightly different starting condition), A249148.

A049084(n) = if(isprime(n), primepi(n), 0); \\ This function from Charles R Greathouse IV
A056239(n) = { my(f); if(1==n, 0, f=factor(n); sum(i=1, #f~, f[i,2] * A049084(f[i,1]))); }
A249337_write_bfile(up_to_n) = { my(counts, n, a_n); counts = vector(up_to_n); a_n = 1; for(n = 1, up_to_n, write("b249337.txt", n, " ", a_n); counts[1+A056239(a_n)]++; if(1 == n, a_n = 2, a_n = counts[1+A056239(a_n)])); };
A249337_write_bfile(12580);

;; With memoization-macro definec from Antti Karttunen's IntSeq-library.
(definec (A249337 n) (if (<= n 2) n (let ((s (A056239 (A249337 (- n 1))))) (let loop ((i (- n 1)) (k 0)) (cond ((zero? i) k) ((= (A056239 (A249337 i)) s) (loop (- i 1) (+ k 1))) (else (loop (- i 1) k))))))) ;; Slow, quadratic time implementation.

a(1) = 1, a(2) = 2; for n>2, a(n) = number of values k in range 1 .. n-1 such that A056239(a(k)) = A056239(a(n-1)).

A249072 Sum of prime indices in the prime factorization of A249337(n), counted with multiplicity: a(n) = A056239(A249337(n)).

Original entry on oeis.org

0, 1, 0, 1, 1, 2, 0, 2, 1, 2, 2, 2, 3, 0, 2, 3, 1, 3, 2, 4, 0, 3, 2, 3, 3, 3, 4, 1, 3, 3, 4, 2, 4, 2, 4, 3, 4, 3, 5, 0, 3, 4, 4, 3, 6, 0, 4, 4, 4, 5, 1, 4, 4, 6, 1, 3, 5, 2, 5, 2, 4, 5, 3, 5, 3, 4, 5, 4, 4, 7, 0, 3, 7, 1, 4, 5, 3, 5, 4, 8, 0, 4, 5, 4, 6, 2, 6, 2, 5, 5, 4, 6, 3, 8, 1, 4, 9, 0

Offset: 1

Antti Karttunen, Oct 26 2014

nonn

Antti Karttunen, Table of n, a(n) for n = 1..12580

Cf. A056239, A249337, A249338.

Cf. A249341 (positions of zeros), A249342 (positions of records).

A049084(n) = if(isprime(n), primepi(n), 0); \\ This function from Charles R Greathouse IV
A056239(n) = { my(f); if(1==n, 0, f=factor(n); sum(i=1, #f~, f[i,2] * A049084(f[i,1]))); }
A249072_write_bfile(up_to_n) = { my(counts, n, a_k, a_n); counts = vector(up_to_n); a_k = 1; for(n = 1, up_to_n, a_n = A056239(a_k); write("b249072_upto12580.txt", n, " ", a_n); counts[1+a_n]++; if(1 == n, a_k = 2, a_k = counts[1+a_n])); };
A249072_write_bfile(12580);

(define (A249072 n) (A056239 (A249337 n)))

a(n) = A056239(A249337(n)).

A249341 Positions of ones in A249337; positions of zeros in A249072.

Original entry on oeis.org

1, 3, 7, 14, 21, 40, 46, 71, 81, 98, 122, 146, 194, 241, 258, 297, 323, 380, 401, 433, 482, 491, 533, 567, 633, 716, 761, 767, 808, 836, 879, 1068, 1105, 1210, 1216, 1370, 1415, 1469, 1515, 1541, 1606, 1684, 1707, 1854, 1872, 1906, 1936, 2117, 2277, 2294, 2305, 2344

Offset: 1

Antti Karttunen, Oct 26 2014

nonn

Antti Karttunen, Table of n, a(n) for n = 1..10000

After the initial term, one more than A249342.

Cf. A249337, A249339, A249072.

allocatemem(234567890);
A049084(n) = if(isprime(n), primepi(n), 0); \\ This function from Charles R Greathouse IV
A056239(n) = { my(f); if(1==n, 0, f=factor(n); sum(i=1, #f~, f[i,2] * A049084(f[i,1]))); }
A249341_write_bfile(up_to_n) = { my(counts, n, k, a_k); counts = vector(min((2^24)-8,up_to_n^2)); n = 0; k = 0; a_k = 1; while(n < up_to_n, k++; if((1 == a_k), n++; write("b249341.txt", n, " ", k)); counts[1+A056239(a_k)]++; if(1 == k, a_k = 2, a_k = counts[1+A056239(a_k)])); };
A249341_write_bfile(10000);

;; With Antti Karttunen's IntSeq-library, two alternative definitions.
(define A249341 (MATCHING-POS 1 1 (lambda (n) (= 1 (A249337 n)))))
(define A249341 (ZERO-POS 1 1 A249072))

For all n >= 2: a(n) = A249342(n) + 1.

cp's OEIS Frontend

A249337 a(1) = 1, a(2) = 2; for n>2, a(n) = number of values k in range 1 .. n-1 such that {sum of prime indices in the prime factorization of a(k)} = {sum of prime indices in the prime factorization of a(n-1)}, both counted with multiplicity.

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A249072 Sum of prime indices in the prime factorization of A249337(n), counted with multiplicity: a(n) = A056239(A249337(n)).

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A249341 Positions of ones in A249337; positions of zeros in A249072.

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