

A242195


Least prime divisor of the nth tangent number T_n which does not divide any T_k with k < n, or 1 if such a primitive prime divisor of T_n does not exist.


7



1, 2, 1, 17, 31, 691, 43, 257, 73, 41, 89, 103, 2731, 113, 151, 37, 43691, 109, 174763, 61681, 337, 59, 178481, 97, 251, 157, 39409, 113161, 67, 1321, 266689, 641, 839, 101, 281, 433, 223, 229, 121369, 631
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OFFSET

1,2


COMMENTS

Conjecture: (i) a(n) is prime for any n > 3.
(ii) For the nth Springer number S_n given by A001586, if n is greater than one and not equal to 5, then S_n has a prime divisor which does not divide any S_k with k < n.
See also A242193 and A242194 for similar conjectures involving Bernoulli numbers and Euler numbers.


LINKS

ZhiWei Sun, Table of n, a(n) for n = 1..54


EXAMPLE

a(4) = 17 since T_4 = 2^4*17 with 17 dividing none of T_1 = 1, T_2 = 2 and T_3 = 2^4.


MATHEMATICA

t[n_]:=(1)^(n1)*2^(2n)(2^(2n)1)BernoulliB[2n]/(2n)
f[n_]:=FactorInteger[t[n]]
p[n_]:=Table[Part[Part[f[n], k], 1], {k, 1, Length[f[n]]}]
Do[If[t[n]<2, Goto[cc]]; Do[Do[If[Mod[t[i], Part[p[n], k]]==0, Goto[aa]], {i, 1, n1}]; Print[n, " ", Part[p[n], k]]; Goto[bb]; Label[aa]; Continue, {k, 1, Length[p[n]]}]; Label[cc]; Print[n, " ", 1]; Label[bb]; Continue, {n, 1, 40}]


PROG

(Sage) # Function LPDtransform is defined in A242193.
def Tnum(n): return (1)^(n1)*2^(2*n)*(2^(2*n)1)*bernoulli(2*n)/(2*n)
A242195list = lambda sup: [LPDtransform(n, Tnum) for n in (1..sup)]
print(A242195list(40)) # Peter Luschny, Jul 26 2019


CROSSREFS

Cf. A000040, A000182, A001586, A242169, A242170, A242171, A242173, A242193, A242194.
Sequence in context: A266827 A316226 A160468 * A012889 A013072 A012895
Adjacent sequences: A242192 A242193 A242194 * A242196 A242197 A242198


KEYWORD

nonn


AUTHOR

ZhiWei Sun, May 07 2014


STATUS

approved



