A336519 Primes in Pi (variant of A336520): a(n) is the smallest prime factor of A090897(n) that does not appear in earlier terms of a, or 1, if no such factor exists.

3, 2, 53, 7, 58979, 161923, 2643383, 1746893, 6971, 5, 17, 1499, 11, 1555077581737, 297707, 13, 37, 126541, 2130276389911155737, 1429, 71971, 383, 61, 1559, 29, 193, 12073, 698543, 157, 20289606809, 23687, 1249, 59, 2393, 251, 101, 15827173, 82351, 661

Offset

1,1

Comments

Inspired by a comment of Mario Cortés in A090897, who suggests that 1 might not appear in this sequence.

Links

Table of n, a(n) for n=1..39.

Peter Luschny, Prime factorization for n = 1..100.

Example

[ 1] 3,          {3}                  -> 3;
[ 2] 14,         {2, 7}               -> 2;
[ 3] 159,        {3, 53}              -> 53;
[ 4] 2653,       {7, 379}             -> 7;
[ 5] 58979,      {58979}              -> 58979;
[ 6] 323846,     {2, 161923}          -> 161923;
[ 7] 2643383,    {2643383}            -> 2643383;
[ 8] 27950288,   {2, 1746893}         -> 1746893;
[ 9] 419716939,  {6971, 60209}        -> 6971;
[10] 9375105820, {2, 5, 1163, 403057} -> 5.

Maple

aList := proc(len) local p, R, spl; R := [];
spl := L -> [seq([seq(L[i], i=1 + n*(n+1)/2..(n+1)*(n+2)/2)], n=0..len)]:
ListTools:-Reverse(convert(floor(Pi*10^((len+1)*(len+2)/2)), base, 10)):
map(`@`(parse, cat, op), spl(%)); map(NumberTheory:-PrimeFactors, %);
for p in % do ListTools:-SelectFirst(p -> evalb(not p in R), p);
R := [op(R), `if`(%=NULL, 1, %)] od end: aList(30);

Mathematica

Block[{nn = 38, s}, s = RealDigits[Pi, 10, (# + 1) (# + 2)/2 &@ nn][[1]]; Nest[Function[{a, n}, Append[a, SelectFirst[FactorInteger[FromDigits@ s[[1 + n (n + 1)/2 ;; (n + 1) (n + 2)/2 ]]][[All, 1]], FreeQ[a, #] &] /. k_ /; MissingQ@ k -> 1]] @@ {#, Length@ #} &, {}, nn + 1]] (* Michael De Vlieger, Aug 21 2020 *)

Prog

(SageMath)
def Select(item, Selected):
    return next((x for x in item if not (x in Selected)), 1)
def PiPart(n):
    return floor(pi * 10^(n * (n + 1) // 2 - 1)) % 10^n
def A336519List(len):
    prev = []
    for n in range(1, len + 1):
        p = prime_factors(PiPart(n))
        prev.append(Select(p, prev))
    return prev
print(A336519List(39))

Crossrefs

Cf. A090897, A336520.

Sequence in context: A331474 A093892 A104254 * A231576 A336520 A190286

Adjacent sequences: A336516 A336517 A336518 * A336520 A336521 A336522

Keyword

nonn,base

Author

Peter Luschny, Aug 21 2020

Status

approved