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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. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 6 21:23 EDT 2021. Contains 343590 sequences. (Running on oeis4.)