A024707 -id:A024707

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A244738

a(n) = (prime(n) mod 5) mod 3.

+10
4

2, 0, 0, 2, 1, 0, 2, 1, 0, 1, 1, 2, 1, 0, 2, 0, 1, 1, 2, 1, 0, 1, 0, 1, 2, 1, 0, 2, 1, 0, 2, 1, 2, 1, 1, 1, 2, 0, 2, 0, 1, 1, 1, 0, 2, 1, 1, 0, 2, 1, 0, 1, 1, 1, 2, 0, 1, 1, 2, 1, 0, 0, 2, 1, 0, 2, 1, 2, 2, 1, 0, 1, 2, 0, 1, 0, 1, 2, 1, 1, 1, 1, 1, 0, 1, 0 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`1,1`
	LINKS	`Clark Kimberling, Table of n, a(n) for n = 1..4000`
	EXAMPLE	`n ... prime(n) mod 5 mod 3` `1 ..... 2 ..... 2 ... 2` `2 ..... 3 ..... 3 ... 0` `3 ..... 5 ..... 0 ... 0` `4 ..... 7 ..... 2 ... 2` `5 ..... 11 .... 1 ... 1` `6 ..... 13 .... 3 ... 0`
	MATHEMATICA	`z = 300; u = Mod[Table[Mod[Prime[n], 5], {n, 1, z}], 3] (* A244738 )` `v1 = Flatten[Position[u, 0]] ( A244739 )` `v2 = Flatten[Position[u, 1]] ( A024707 )` `v3 = Flatten[Position[u, 2]] ( A244741 )` `Mod[Mod[Prime[Range[90]], 5], 3] ( Harvey P. Dale, Aug 14 2019 *)`
	CROSSREFS	`Cf. A039703, A244739, A024707, A244741, A244735.`
	KEYWORD	`nonn,easy`
	AUTHOR	`Clark Kimberling, Jul 05 2014`
	STATUS	`approved`

A244739

Numbers k such that (prime(k) mod 5) == 0 (mod 3).

+10
4

2, 3, 6, 9, 14, 16, 21, 23, 27, 30, 38, 40, 44, 48, 51, 56, 61, 62, 65, 71, 74, 76, 84, 86, 90, 96, 99, 103, 108, 112, 117, 119, 122, 124, 130, 132, 137, 143, 147, 150, 153, 162, 166, 170, 174, 179, 183, 185, 188, 191, 192, 196, 198, 200, 208, 213, 220, 224 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`1,1`
	COMMENTS	`Every positive integer is in exactly one of the sequences A244739, A024707, A244741.`
	LINKS	`Clark Kimberling, Table of n, a(n) for n = 1..1000`
	EXAMPLE	`n ... prime(n) mod 5 mod 3` `1 ..... 2 ..... 2 ... 2` `2 ..... 3 ..... 3 ... 0` `3 ..... 5 ..... 0 ... 0` `4 ..... 7 ..... 2 ... 2` `5 ..... 11 .... 1 ... 1` `6 ..... 13 .... 3 ... 0`
	MATHEMATICA	`z = 300; u = Mod[Table[Mod[Prime[n], 5], {n, 1, z}], 3] (* A244738 )` `v1 = Flatten[Position[u, 0]] ( A244739 )` `v2 = Flatten[Position[u, 1]] ( A024707 )` `v3 = Flatten[Position[u, 2]] ( A244741 *)`
	CROSSREFS	`Cf. A039703, A244738, A024707, A244741, A244735. Essentially the same as A049508.`
	KEYWORD	`nonn,easy`
	AUTHOR	`Clark Kimberling, Jul 05 2014`
	STATUS	`approved`

A244741

Numbers k such that (prime(k) mod 5) == 2 (mod 3).

+10
4

1, 4, 7, 12, 15, 19, 25, 28, 31, 33, 37, 39, 45, 49, 55, 59, 63, 66, 68, 69, 73, 78, 88, 91, 93, 101, 102, 106, 107, 111, 113, 118, 123, 129, 134, 138, 139, 144, 148, 151, 154, 155, 159, 161, 163, 165, 168, 181, 184, 187, 195, 199, 203, 206, 211, 214, 217 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`1,2`
	COMMENTS	`Every positive integer is in exactly one of the sequences A244739, A024707, A244741.`
	LINKS	`Clark Kimberling, Table of n, a(n) for n = 1..1000`
	EXAMPLE	`n ... prime(n) mod 5 mod 3` `1 ..... 2 ..... 2 ... 2` `2 ..... 3 ..... 3 ... 0` `3 ..... 5 ..... 0 ... 0` `4 ..... 7 ..... 2 ... 2` `5 ..... 11 .... 1 ... 1` `6 ..... 13 .... 3 ... 0`
	MAPLE	A244741:=n->`if`(((ithprime(n) mod 5) mod 3) = 2, n, NULL): seq(A244741(n), n=1..250); # Wesley Ivan Hurt, Jul 06 2014
	MATHEMATICA	`z = 300; u = Mod[Table[Mod[Prime[n], 5], {n, 1, z}], 3] (* A244738 )` `v1 = Flatten[Position[u, 0]] ( A244739 )` `v2 = Flatten[Position[u, 1]] ( A024707 )` `v3 = Flatten[Position[u, 2]] ( A244741 *)`
	CROSSREFS	`Cf. A039703, A244738, A244739, A024707, A244735. Essentially the same as A049509.`
	KEYWORD	`nonn,easy`
	AUTHOR	`Clark Kimberling, Jul 05 2014`
	STATUS	`approved`

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Last modified August 30 15:13 EDT 2024. Contains 375545 sequences. (Running on oeis4.)