A375753 -id:A375753 - cp's OEIS frontend

A375752 a(n) is the difference between T=n*(n+1)/2 and the largest prime not exceeding T.

0, 1, 3, 2, 2, 5, 5, 2, 2, 5, 5, 2, 2, 7, 5, 2, 4, 9, 11, 2, 2, 5, 7, 8, 2, 5, 5, 2, 2, 5, 5, 4, 2, 11, 5, 2, 2, 7, 9, 2, 16, 5, 7, 2, 12, 5, 5, 2, 16, 5, 5, 2, 2, 9, 13, 16, 2, 11, 7, 2, 2, 5, 11, 2, 4, 5, 5, 4, 8, 5, 7, 2, 8, 7, 9, 2, 2, 23, 11, 2, 12, 17, 11, 12, 2

Offset: 2

Hugo Pfoertner, Aug 26 2024

Cf. A000217, A007917, A065384, A075402, A375753, A375754.

Table[T=n(n+1)/2;T-If[PrimeQ[T],T,NextPrime[T,-1]],{n,2,86}] (* James C. McMahon, Sep 27 2024 *)

a(n) = my(t=n*(n+1)/2); t - precprime(t)

from sympy import prevprime
def A375752(n): return (t:=n*(n+1)//2) - prevprime(t) # Karl-Heinz Hofmann, Aug 27 2024

a(n) = A000217(n) - A065384(n). - Michel Marcus, Aug 27 2024

A375754 a(n) is the difference between the next greater square of a prime and n*(n+1)/2.

Original entry on oeis.org

4, 3, 1, 3, 15, 10, 4, 21, 13, 4, 66, 55, 43, 30, 16, 1, 33, 16, 118, 99, 79, 58, 36, 13, 61, 36, 10, 151, 123, 94, 64, 33, 1, 280, 246, 211, 175, 138, 100, 61, 21, 100, 58, 15, 379, 334, 288, 241, 193, 144, 94, 43, 303, 250, 196, 141, 85, 28, 138, 79, 19, 318, 256

Offset: 0

Hugo Pfoertner, Aug 26 2024

			a(0) = A001248(1) - A000217(0) = 2^2 - 0 = 4,
a(1) = A001248(1) - A000217(1) = 2^2 - 1 = 3,
a(2) = A001248(1) - A000217(2) = 2^2 - 3 = 1,
a(3) = A001248(2) - A000217(3) = 3^2 - 6 = 3.

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Cf. A000217, A001248, A075402, A375752, A375753.

NextPrime[Sqrt[#]]^2-#&/@Accumulate[Range[0,70]] (* Harvey P. Dale, Feb 16 2025 *)

a375754(n) = my(t=n*(n+1)/2, s=sqrtint(t), p=nextprime(s)); if(p^2-t < 0, p=nextprime(p+1)); p^2-t

A375751 a(n) is the difference between F=A000045(n) and the largest prime not exceeding F.

Original entry on oeis.org

0, 0, 0, 1, 0, 2, 3, 2, 0, 5, 0, 4, 3, 4, 0, 5, 4, 2, 7, 4, 0, 17, 8, 14, 31, 14, 0, 37, 20, 26, 9, 20, 22, 11, 6, 12, 15, 32, 18, 17, 0, 16, 43, 24, 0, 17, 20, 26, 27, 20, 6, 9, 12, 34, 29, 36, 30, 47, 48, 4, 45, 32, 54, 27, 132, 22, 31, 4, 32, 11, 12, 60, 7, 76

Offset: 3

Hugo Pfoertner, Aug 27 2024

Amiram Eldar, Table of n, a(n) for n = 3..10000

Cf. A000045, A007917, A001605, A138184, A138185, A159977, A159978, A202090.

a:= n-> (F-> F-prevprime(F+1))(combinat[fibonacci](n)):
seq(a(n), n=3..76);  # Alois P. Heinz, Aug 27 2024

a[n_]:=Module[{p=2},While[(f=Fibonacci[n])>=p, pold=p;p=NextPrime[p]]; d=f-pold;If[d>0,f-pold,d=0]; d]; Array[a,74,3] (* Stefano Spezia, Aug 27 2024 *)
Map[(# - NextPrime[# + 1, -1]) &, Fibonacci[Range[3, 76]]] (* Amiram Eldar, Aug 29 2024 *)

a(n) = my(F=fibonacci(n)); F-precprime(F)

from sympy import prevprime, fibonacci
def A375753(n): return (F:=fibonacci(n)) - prevprime(F+1) # Karl-Heinz Hofmann, Aug 27 2024

a(n) = A000045(n) - A138184(n).

a(n) = 0 <=> n in { A001605 }. - Alois P. Heinz, Aug 27 2024

cp's OEIS Frontend

A375752 a(n) is the difference between T=n*(n+1)/2 and the largest prime not exceeding T.

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A375754 a(n) is the difference between the next greater square of a prime and n*(n+1)/2.

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A375751 a(n) is the difference between F=A000045(n) and the largest prime not exceeding F.

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