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A317945 Filter sequence constructed from the coefficients of the Stern polynomials B(d,t) collected for each divisor d of n. Restricted growth sequence transform of A317944. 4
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Differs from A000027(n) = n (positive integers) from a(193) = 191 on.

For all i, j: a(i) = a(j) => A317838(i) = A317838(j).

There are certain prime pairs p, q for which the Stern polynomials B(p,t) and B(q,t) (see table A125184) have equal multisets of nonzero coefficients. For example, for primes 191 and 193 these coefficients are {1, 2, 2, 2, 2, 3, 1} and {1, 2, 2, 2, 3, 2, 1} (from which follows that A278243(191) = A278243(193), A286378(191) = A286378(193) and thus => a(191) = a(193) => A002487(191) = A002487(193) as well). Other such prime pairs currently known are {419, 461}, {2083, 2143} and {11777, 12799}. Whenever a(p) = a(q) for such a prime pair, then also a(2^k * p) = a(2^k * q) for all k >= 0. It would be nice to know whether there could exist any other cases of a(i) = a(j), i != j, but for example both i and j being odd semiprimes?

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for sequences related to Stern's sequences

PROG

(PARI) \\ Needs also code from A286378.

up_to = 65537;

A317944(n) = { my(m=1); fordiv(n, d, if(d>1, m *= prime(A286378(d)-1))); (m); };

v317945 = rgs_transform(vector(up_to, n, A317944(n)));

A317945(n) = v317945[n];

CROSSREFS

Cf. A002487, A125184, A260443, A286378, A317943, A317944.

Cf. also A305795, A317838.

Sequence in context: A001477 A087156 A254109 * A292579 A262530 A291179

Adjacent sequences:  A317942 A317943 A317944 * A317946 A317947 A317948

KEYWORD

nonn

AUTHOR

Antti Karttunen, Aug 12 2018

STATUS

approved

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Last modified October 15 22:25 EDT 2019. Contains 328038 sequences. (Running on oeis4.)