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A295607
a(n) = A001567(n) - 2^floor(log_2(A001567(n))).
1
85, 49, 133, 81, 363, 705, 881, 1023, 417, 653, 773, 1229, 1985, 273, 275, 585, 1365, 2505, 3861, 129, 289, 719, 2069, 2393, 3113, 4609, 5549, 5555, 5789, 6299, 7517, 7649, 321, 2321, 2337, 3567, 6617, 6993, 9377, 12957, 13737, 14505, 15033, 15225, 15237, 385, 2177, 2565, 7097, 8273, 8897
OFFSET
1,1
COMMENTS
This sequence contains the distances from pseudoprime numbers (A001567) to the next smaller number of the form 2^n. Conjecture: It seems that these distances do not take all possible values. So, if we know that a certain distance does not appear with pseudoprime numbers, we are able to calculate these numbers using Fermat's little theorem and we know for sure that they are primes.
EXAMPLE
There are no pseudoprimes detected by Fermat's little theorem for 2^k+m with m = {3,5,7,...,47} up to k = 10000 (checked using the Pari function ispseudoprime(k)). When this sequence is ordered for the first 10^5 pseudoprimes, the following first terms (up to 1000) result: 1, 49, 81, 85, 129, 133, 273, 275, 289, 321, 363, 385, 417, 585, 653, 705, 719, 773, 881.
MATHEMATICA
Map[# - 2^Floor@ Log2@ # &, Select[Range[3, 10^5, 2], And[! PrimeQ[#], PowerMod[2, (# - 1), #] == 1] &]] (* Michael De Vlieger, Nov 26 2017 *)
PROG
(PARI) a(A001567)=A001567-2^(floor(log(A001567)/log(2))) \\
CROSSREFS
Cf. A001567.
Sequence in context: A317438 A105328 A033405 * A003906 A215432 A020312
KEYWORD
nonn
AUTHOR
Jonas Kaiser, Nov 24 2017
STATUS
approved