A209261
a(n) = n^13 + 13*n + 13^n.
Original entry on oeis.org
1, 27, 8387, 1596559, 67137477, 1221074483, 13065520903, 96951759015, 550571544713, 2552470327819, 10137858491979, 36314872538111, 130291290501709, 605750213184675, 4731091158953615, 53132088082450327, 669920208810550545
Offset: 0
a(2) = 2^13 + 13*2 + 13^2 = 8387.
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[n^13 + 13*n + 13^n: n in [0..30]]; // G. C. Greubel, Jan 05 2018
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Table[n^13 + 13*n + 13^n, {n,0,30}] (* G. C. Greubel, Jan 05 2018 *)
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makelist(n^13 + 13*n + 13^n,n,0,20); /* Martin Ettl, Jan 15 2013 */
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for(n=0,30, print1(n^13 + 13*n + 13^n, ", ")) \\ G. C. Greubel, Jan 05 2018
A017579
a(n) = (12n+4)^11.
Original entry on oeis.org
4194304, 17592186044416, 8293509467471872, 419430400000000000, 7516865509350965248, 73786976294838206464, 488595558857835544576, 2450808588882738675712, 10000000000000000000000, 34785499933455142617088, 106570876280498368282624, 294393347626373780340736
Offset: 0
- Index entries for linear recurrences with constant coefficients, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).
A356645
a(n) = tau(n)^2 - 4*n^11 where tau is Ramanujan's tau function A000594.
Original entry on oeis.org
-3, -7616, -645084, -14610432, -171983600, -1414609920, -7628945436, -27222867968, -112609506987, -386562553600, -855436691900, -2834434031616, -6834860379504, -16036772433920, -33117544971900, -69394306695168, -89395660818176, -249634755002304, -352295159176476, -768651312742400
Offset: 1
- Guillaume Duval, Théorème de Chebotarev et Congruences de suites récurrentes linéaires, liens avec les algorithmes de factorisations sur Fp, arXiv:2208.08899 [math.NT], 2022. See Corollaire 20 p. 12. In French.
- J. P. Serre, An interpretation of some congruences concerning Ramanujan's tau function, Séminaire Delange-Pisot-Poitou. Théorie des nombres, tome 9, no 1 (1967-1968), exp. no 14, pp. 1-17.
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a[n_] := RamanujanTau[n]^2 - 4*n^11; Array[a, 20] (* Amiram Eldar, Aug 19 2022 *)
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a(n) = ramanujantau(n)^2 - 4*n^11; \\ Michel Marcus, Aug 19 2022
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