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A260442 Sequence A260443 sorted into ascending order. 8
1, 2, 3, 5, 6, 7, 11, 13, 15, 17, 18, 19, 23, 29, 30, 31, 35, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 75, 77, 79, 83, 89, 90, 97, 101, 103, 105, 107, 109, 113, 127, 131, 137, 139, 143, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 210, 211, 221, 223, 227, 229, 233, 239, 241, 245, 251, 257, 263, 269, 270, 271, 277, 281, 283, 293, 307, 311 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Each term is a prime factorization encoding of one of the Stern polynomials. See A260443 for details.

Numbers n for which A260443(A048675(n)) = n. - Antti Karttunen, Oct 14 2016

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..10000

PROG

(PARI)

allocatemem(2^30);

A048675(n) = my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; \\ Michel Marcus, Oct 10 2016

A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From Michel Marcus

A260443(n) = if(n<2, n+1, if(n%2, A260443(n\2)*A260443(n\2+1), A003961(A260443(n\2))));

isA260442(n) = (A260443(A048675(n)) == n);  \\ The most naive version.

A055396(n) = if(n==1, 0, primepi(factor(n)[1, 1])) \\ Charles R Greathouse IV, Apr 23 2015

A061395(n) =  if(1==n, 0, primepi(vecmax(factor(n)[, 1]))); \\ After M. F. Hasler's code for A006530.

isA260442(n) = ((1==n) || isprime(n) || ((omega(n) == 1+(A061395(n)-A055396(n))) && (A260443(A048675(n)) == n))); \\ Somewhat optimized.

i=0; n=0; while(i < 10001, n++; if(isA260442(n), write("b260442.txt", i, " ", n); i++));

(Scheme, with Antti Karttunen's IntSeq-library)

(define A260442 (FIXED-POINTS 0 1 (COMPOSE A260443 A048675)))

;; An optimized version:

(define A260442 (MATCHING-POS 0 1 (lambda (n) (or (= 1 n) (= 1 (A010051 n)) (and (not (< (A001221 n) (+ 1 (A243055 n)))) (= n (A260443 (A048675 n))))))))

(Python)

from sympy import factorint, prime, primepi

from operator import mul

def a048675(n):

    F=factorint(n)

    return 0 if n==1 else sum([F[i]*2**(primepi(i) - 1) for i in F])

def a003961(n):

    F=factorint(n)

    return 1 if n==1 else reduce(mul, [prime(primepi(i) + 1)**F[i] for i in F])

def a(n): return n + 1 if n<2 else a003961(a(n/2)) if n%2==0 else a((n - 1)/2)*a((n + 1)/2)

print [n for n in xrange(301) if a(a048675(n))==n] # Indranil Ghosh, Jun 21 2017

CROSSREFS

Cf. A003961, A048675, A260443.

Subsequence of A073491.

From 2 onward the positions of nonzeros in A277333.

Various subsequences: A000040, A002110, A070826, A277317, A277200 (even terms).  Also all terms of A277318 are included here.

Cf. also A277323, A277324 and permutation pair A277415 & A277416.

Sequence in context: A325100 A053329 A308420 * A098962 A073485 A062101

Adjacent sequences:  A260439 A260440 A260441 * A260443 A260444 A260445

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jul 29 2015

EXTENSIONS

Pari and Scheme program code added by Antti Karttunen, Oct 14 2016

STATUS

approved

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Last modified July 16 04:09 EDT 2019. Contains 325064 sequences. (Running on oeis4.)