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A289631 Prime powers P for which the number of modulo P residues among sums of two sixth powers is less than P. 3
4, 7, 8, 9, 13, 16, 19, 27, 31, 32, 37, 43, 49, 61, 64, 67, 73, 79, 81, 109, 121, 128, 139, 169, 223, 243, 256, 343, 361, 512, 529, 729, 961, 1024, 1331, 1369, 1849, 2048, 2187, 2197, 2209, 2401, 3481, 3721, 4096, 4489, 5041, 5329, 6241, 6561, 6859, 6889, 8192 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Numbers P in A246655 (prime powers) for which A289630(P) < P.

Every number > 3 that is a power of 2, 3, or 7 is in the sequence.

Primes in this sequence begin 7, 13, 19, 31, 37, 43, 61, 67, 73, 79, 109, 139, 223.

Conjecture: 223 is the final prime in this sequence.

From Jon E. Schoenfield, Jul 14 2017: (Start)

If any prime power P = p^k (where p is prime and k >= 1) is in the sequence, then so is p^j for all j > k.

Conjecture: the terms in this sequence that are the squares of primes are the squares of 13, 37, 61, 73, 109, and every prime not congruent to 1 mod 4.

(End)

LINKS

Giovanni Resta, Table of n, a(n) for n = 1..192 (terms < 2*10^6)

EXAMPLE

7 is in the sequence because A289630(7) = 3 < 7.

5 is not in the sequence because A289630(5) = 5.

A289630(12) = 9 < 12, but 12 is not in the sequence because it is not a prime power.

PROG

(PARI) isok(n) = isprimepower(n) && (#Set(vector(n^2, i, ((i%n)^6 + (i\n)^6) % n)) < n); \\ Michel Marcus, Jul 11 2017

CROSSREFS

Cf. A246655 (prime powers), A289630 (Number of modulo n residues among sums of two sixth powers).

Cf. A289740 (similar sequence for sums of three sixth powers), A289760 (similar sequence for sums of four sixth powers). - Jon E. Schoenfield, Jul 14 2017

Sequence in context: A047538 A074231 A310938 * A076680 A235623 A001074

Adjacent sequences:  A289628 A289629 A289630 * A289632 A289633 A289634

KEYWORD

nonn

AUTHOR

Jon E. Schoenfield, Jul 08 2017

STATUS

approved

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Last modified October 24 02:02 EDT 2021. Contains 348217 sequences. (Running on oeis4.)