Real function resembling a sequence of numbers given by $(f(n)+P(n))mod{(Q(n))}$ [closed]

A while ago I have asked this question:here about the nature of a certain series which turns out it is divergent in most cases. Now I'm interested about the numbers yielded by nominators of such series.Here are 3 examples of the first 100 numbers of such sequence of numbers.

1. for the nominator $$(2^n+3^n+n^4+6n^3+13n^2+129n+17)\bmod(n^2+15n+26)$$ the following string is yielded:{3, 44, 79, 50, 117, 84, 51, 116, 207, 20, 159, 278, 9, 332, 355, 272, 201, 552, 519, 650, 75, 284, 639, 782, 447, 212, 471, 386, 777, 924, 1071, 818, 899, 1424, 711, 1358, 1851, 1052, 1495, 926, 45, 1464, 1599, 218, 1323, 1388, 1671, 246, 1467, 2132, 2951, 218, 3609, 2084, 1095, 2420, 3841, 692, 1071, 432, 141, 2204, 4039, 536, 3945, 4280, 5511, 2816, 5519, 4556, 4683, 4628, 219, 3668, 87, 3230, 5481, 6972, 4659, 2282, 1177, 464, 7719, 3694, 45, 3212, 8131, 7346, 4695, 2828, 8247, 6878, 9219, 9884, 4743, 9350, 7341, 5312, 1783, 488}
2. for the nominator $$(2^n+3^n+n^4+5n^3+15n^2+167n+49)\bmod(n^2+14n+33)$$ the following string is yielded: {2, 57, 12, 55, 96, 17, 104, 143, 48, 214, 296, 221, 224, 341, 456, 487, 224, 86, 68, 21, 0, 667, 672, 665, 320, 998, 924, 388, 288, 500, 1004, 216, 1536, 541, 1172, 1295, 704, 389, 168, 2029, 800, 2087, 500, 1730, 96, 2764, 2344, 1739, 128, 1318, 1644, 676, 1920, 1721, 2612, 3112, 1824, 136, 2828, 2060, 3488, 3022, 2172, 1135, 3136, 413, 5024, 1572, 5568, 406, 5852, 5141, 3776, 2806, 3096, 4117, 2144, 5309, 4748, 5912, 336, 1087, 3120, 530, 5888, 2109, 2364, 5095, 7408, 8900, 9116, 6976, 7200, 8971, 7912, 5174, 4064, 5810, 5988, 10390}
3. for the nominator $$(2^n+3^n+n^4+4n^3+47n^2+229n+11)\bmod(n^2+12n+35)$$ the following string is yielded: {9, 25, 65, 11, 11, 24, 93, 67, 159, 239, 17, 33, 195, 157, 101, 221, 215, 273, 441, 43, 627, 317, 245, 239, 591, 124, 769, 647, 1043, 1169, 1149, 1225, 855, 257, 41, 1372, 843, 1078, 693, 1073, 2015, 1644, 1425, 1012, 1291, 1031, 845, 2067, 2823, 2434, 2889, 3095, 1235, 1740, 2181, 2950, 2735, 2468, 2465, 1988, 3603, 2422, 725, 3824, 791, 2258, 1977, 1357, 339, 1214, 5357, 1862, 3135, 2581, 2801, 2558, 4955, 4798, 2229, 508, 4759, 5798, 3545, 5200, 4371, 5821, 6189, 7652, 1871, 8319, 4545, 4822, 5955, 4520, 2741, 6351, 6087, 3328, 7481, 788}

The above calculations have been done with wolfram alpha. These numbers given in those strings have an appearance of random even if they are not. I'm interested in such lists of numbers. But my question for today is: Is there a way to generate a real function that resembles such a process?