Displaying 1-10 of 15 results found.
Primes of the form 4*k + 3.
(Formerly M2624 N1039)
+10
338
3, 7, 11, 19, 23, 31, 43, 47, 59, 67, 71, 79, 83, 103, 107, 127, 131, 139, 151, 163, 167, 179, 191, 199, 211, 223, 227, 239, 251, 263, 271, 283, 307, 311, 331, 347, 359, 367, 379, 383, 419, 431, 439, 443, 463, 467, 479, 487, 491, 499, 503, 523, 547, 563, 571
CROSSREFS
Apart from initial term, same as A045326.
Mersenne numbers: 2^p - 1, where p is prime.
(Formerly M2694 N1079)
+10
123
3, 7, 31, 127, 2047, 8191, 131071, 524287, 8388607, 536870911, 2147483647, 137438953471, 2199023255551, 8796093022207, 140737488355327, 9007199254740991, 576460752303423487, 2305843009213693951, 147573952589676412927, 2361183241434822606847
Nonhypotenuse numbers (indices of positive squares that are not the sums of 2 distinct nonzero squares).
(Formerly M0542)
+10
44
1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 14, 16, 18, 19, 21, 22, 23, 24, 27, 28, 31, 32, 33, 36, 38, 42, 43, 44, 46, 47, 48, 49, 54, 56, 57, 59, 62, 63, 64, 66, 67, 69, 71, 72, 76, 77, 79, 81, 83, 84, 86, 88, 92, 93, 94, 96, 98, 99, 103, 107, 108, 112, 114, 118, 121, 124, 126, 127
CROSSREFS
The subsequence of primes is A045326.
Number of divisors of n over the Gaussian integers.
+10
20
1, 3, 2, 5, 4, 6, 2, 7, 3, 12, 2, 10, 4, 6, 8, 9, 4, 9, 2, 20, 4, 6, 2, 14, 9, 12, 4, 10, 4, 24, 2, 11, 4, 12, 8, 15, 4, 6, 8, 28, 4, 12, 2, 10, 12, 6, 2, 18, 3, 27, 8, 20, 4, 12, 8, 14, 4, 12, 2, 40, 4, 6, 6, 13, 16, 12, 2, 20, 4, 24, 2, 21, 4, 12, 18, 10, 4, 24, 2, 36, 5, 12, 2, 20, 16, 6
FORMULA
Presumably a(n) = 2 iff n is a rational prime == 3 mod 4 (see A045326). - N. J. A. Sloane, Jan 07 2003, Feb 23 2007
Second least-significant bit in the binary expansion of the n-th prime.
+10
8
1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1
COMMENTS
a(n)=1 iff prime(n) is a member of A045326 (equivalently for n>1, iff prime(n)-3 is divisible by 4).
Primes congruent to {2, 3, 5, 7} mod 11.
+10
7
2, 3, 5, 7, 13, 29, 47, 71, 73, 79, 101, 113, 137, 139, 157, 167, 179, 181, 211, 223, 227, 233, 269, 271, 277, 293, 311, 313, 337, 359, 379, 401, 409, 421, 431, 443, 467, 487, 491, 509, 541, 557, 563, 577, 599, 601, 607, 619, 641, 643, 673, 709, 733, 739, 751
CROSSREFS
Cf. A003627, A045326, A003631, A045309, A045314, A042987, A078403, A042993, A167134, A167135, A167119: primes p such that p mod k is prime, for k = 3..13 resp.
Primes congruent to {2, 3, 5, 7, 11} mod 12.
+10
7
2, 3, 5, 7, 11, 17, 19, 23, 29, 31, 41, 43, 47, 53, 59, 67, 71, 79, 83, 89, 101, 103, 107, 113, 127, 131, 137, 139, 149, 151, 163, 167, 173, 179, 191, 197, 199, 211, 223, 227, 233, 239, 251, 257, 263, 269, 271, 281, 283, 293, 307, 311, 317, 331, 347, 353, 359
CROSSREFS
Cf. A003627, A045326, A003631, A045309, A045314, A042987, A078403, A042993, A167134, A167135, A167119: primes p such that p mod k is prime, for k = 3..13 resp.
a(n) = n^3 + (n+1)*(n+2).
+10
6
2, 7, 20, 47, 94, 167, 272, 415, 602, 839, 1132, 1487, 1910, 2407, 2984, 3647, 4402, 5255, 6212, 7279, 8462, 9767, 11200, 12767, 14474, 16327, 18332, 20495, 22822, 25319, 27992, 30847, 33890, 37127, 40564, 44207, 48062, 52135, 56432, 60959, 65722, 70727, 75980, 81487, 87254
COMMENTS
The primes in the sequence belong to A045326.
Primes congruent to 2, 3, 5, 7 or 11 (mod 13).
+10
5
2, 3, 5, 7, 11, 29, 31, 37, 41, 59, 67, 83, 89, 107, 109, 137, 163, 167, 193, 197, 211, 223, 239, 241, 263, 271, 293, 317, 349, 353, 367, 379, 397, 401, 419, 421, 431, 449, 457, 479, 499, 509, 523, 557, 577, 587, 601, 613, 631, 653, 661, 683, 691, 709, 733, 739, 743, 757
CROSSREFS
Cf. A003627, A045326, A003631, A045309, A045314, A042987, A078403, A042993, A167134, A167135: primes p such that p mod k is prime, for k = 3..12 resp.
1, 2, 6, 10, 18, 22, 30, 42, 46, 58, 66, 70, 78, 82, 102, 106, 126, 130, 138, 150, 162, 166, 178, 190, 198, 210, 222, 226, 238, 250, 262, 270, 282, 306, 310, 330, 346, 358, 366, 378, 382, 418, 430, 438, 442, 462, 466, 478, 486, 490, 498, 502, 522, 546, 562
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