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
Examples
[ 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.
Links
- Peter Luschny, Prime factorization for n = 1..100.
Programs
-
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 *) -
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))
Comments