A161896 -id:A161896

Search: a161896 -id:a161896

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A005384

Sophie Germain primes p: 2p+1 is also prime.
(Formerly M0731)

+10
419

2, 3, 5, 11, 23, 29, 41, 53, 83, 89, 113, 131, 173, 179, 191, 233, 239, 251, 281, 293, 359, 419, 431, 443, 491, 509, 593, 641, 653, 659, 683, 719, 743, 761, 809, 911, 953, 1013, 1019, 1031, 1049, 1103, 1223, 1229, 1289, 1409, 1439, 1451, 1481, 1499, 1511, 1559

(list; graph; refs; listen; history; text; internal format)

A161897

Prime numbers p for which k = (3^p - 3 * 3^((p + 1) / 2) - 6p + 6) / (3p^2 - 3p) is an integer

+10
5

11, 23, 47, 59, 83, 107, 167, 179, 227, 263, 347, 359, 383, 467, 479, 503, 563, 587, 719, 839, 863, 887, 983, 1019, 1187, 1283, 1307, 1319, 1367, 1439, 1487, 1523, 1619, 1823, 1907, 2027, 2039, 2063, 2099, 2207, 2447, 2459, 2579, 2819, 2879, 2903, 2963, 2999

(list; graph; refs; listen; history; text; internal format)

A162587

Prime numbers p = 8n + 7 for which k = (7 * (256^n - 16^n) + n^2) / (n * p) is an integer

+10
2

23, 31, 47, 71, 79, 103, 127, 151, 167, 199, 223, 263, 367, 439, 487, 607, 631, 647, 727, 823, 887, 967, 1031, 1087, 1303, 1327, 1367, 1447, 1543, 1567, 1607, 1879, 1951, 2207, 2311, 2503, 2647, 2671, 2887, 3079, 3271, 3463, 3527, 3607, 3727, 3847, 3967

(list; graph; refs; listen; history; text; internal format)

A162586

Integers n for which k = (7 * (256^n - 16^n) + n^2) / (n * (8n + 7)) is an integer

+10
1

2, 3, 5, 8, 9, 12, 15, 18, 20, 24, 27, 32, 45, 54, 60, 75, 78, 80, 90, 102, 110, 120, 128, 135, 162, 165, 170, 180, 192, 195, 200, 234, 243, 275, 288, 312, 330, 333, 360, 384, 408, 432, 440, 450, 465, 480, 495, 500, 513, 540, 612, 620, 624, 675, 684, 702, 729

(list; graph; refs; listen; history; text; internal format)

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