A204916 -id:A204916 - cp's OEIS frontend

A204919 a(n) = q^2 where q is the least prime such that n divides A204916(n)^2 - q^2.

4, 9, 4, 9, 4, 25, 4, 9, 4, 9, 4, 25, 4, 9, 4, 9, 4, 49, 4, 9, 4, 25, 289, 25, 4, 49, 4, 9, 4, 49, 4, 25, 4, 121, 9, 49, 961, 49, 4, 9, 4, 121, 4, 25, 4, 289, 1681, 25, 4, 361, 4, 49, 2209, 529, 4, 9, 4, 289, 4, 49

Offset: 1

Clark Kimberling, Jan 20 2012

nonn

For a guide to related sequences, see A204892.

Original name was "Least prime q^2 such that n divides p^2-q^2 for some prime p>q", which would be A089090. - Robert Israel, May 04 2019

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A089090, A204916, A204908, A204900, A204892.

N:= 100: # to get a(1)..a(N)
A:= Vector(N): count:= 0:
p:= 2: P:= 2:
for i from 1 while count < N do
  p:= nextprime(p);
  ps:= p^2;
  P:= P, p;
  for j from 1 to i while count < N do
   qs:= P[j]^2;
   S:= convert(select(t -> t <= N and A[t]=0, numtheory:-divisors(ps-qs)),list);
   A[S]:= qs;
   count:= count + nops(S);
od od:
convert(A,list); # Robert Israel, May 04 2019

Mathematica
```
(See the program at A204916.)
```

Name corrected by Robert Israel, May 04 2019

A204914 Ordered differences of squared primes.

Original entry on oeis.org

5, 21, 16, 45, 40, 24, 117, 112, 96, 72, 165, 160, 144, 120, 48, 285, 280, 264, 240, 168, 120, 357, 352, 336, 312, 240, 192, 72, 525, 520, 504, 480, 408, 360, 240, 168, 837, 832, 816, 792, 720, 672, 552, 480, 312, 957, 952, 936, 912, 840, 792, 672

Offset: 1

Clark Kimberling, Jan 20 2012

nonn

For a guide to related sequences, see A204892.

			a(1) = s(2) - s(1) =  9 - 4 =  5;
a(2) = s(3) - s(1) = 25 - 4 = 21;
a(3) = s(3) - s(2) = 25 - 9 = 16;
a(4) = s(4) - s(1) = 49 - 4 = 45.

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Cf. A204908, A204900, A204892.

Mathematica
```
(See the program at A204916.)
```

from math import isqrt
from sympy import prime, primerange
def aupton(terms):
  sqps = [p*p for p in primerange(1, prime(isqrt(2*terms)+1)+1)]
  return [b-a for i, b in enumerate(sqps) for a in sqps[:i]][:terms]
print(aupton(52)) # Michael S. Branicky, May 21 2021

A204915 Least k such that n divides A204914(k), the k-th difference of two squared primes.

Original entry on oeis.org

1, 3, 2, 3, 1, 6, 2, 3, 4, 5, 11, 6, 7, 8, 4, 3, 22, 10, 16, 5, 2, 18, 43, 6, 29, 25, 37, 8, 46, 14, 37, 9, 11, 33, 17, 10, 89, 49, 7, 5, 79, 20, 67, 18, 4, 43, 118, 9, 92, 53, 22, 25, 135, 54, 11, 8, 16, 73, 137, 14

Offset: 1

Clark Kimberling, Jan 20 2012

nonn

For a guide to related sequences, see A204892.

Cf. A204908, A204900, A204892.

Mathematica
```
(See the program at A204916.)
```

A204917 Least j such that n divides s(k)-s(j) for some k>j, where s(j)=(prime(j))^2.

Original entry on oeis.org

1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 4, 1, 2, 1, 3, 7, 3, 1, 4, 1, 2, 1, 4, 1, 3, 1, 5, 2, 4, 11, 4, 1, 2, 1, 5, 1, 3, 1, 7, 13, 3, 1, 8, 1, 4, 15, 9, 1, 2, 1, 7, 1, 4

Offset: 1

Clark Kimberling, Jan 20 2012

nonn

For a guide to related sequences, see A204892.

Cf. A204916, A204908, A204900, A204892.

Mathematica
```
(See the program at A204916.)
```

A204918 Least prime p^2 such that n divides p^2-q^2 for some prime q satisfying q

Original entry on oeis.org

9, 25, 25, 25, 9, 49, 25, 25, 49, 49, 169, 49, 121, 121, 49, 25, 361, 121, 289, 49, 25, 289, 841, 49, 529, 361, 841, 121, 961, 169, 841, 121, 169, 529, 289, 121, 1849, 961, 121, 49, 1849, 289, 1681, 289, 49, 841, 2809, 121, 2209, 961, 361, 361, 3481

Offset: 1

Clark Kimberling, Jan 20 2012

nonn

For a guide to related sequences, see A204892.

Cf. A204916, A204908, A204900, A204892.

Mathematica
```
(See the program at A204916.)
```

cp's OEIS Frontend

A204919 a(n) = q^2 where q is the least prime such that n divides A204916(n)^2 - q^2.

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A204914 Ordered differences of squared primes.

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A204915 Least k such that n divides A204914(k), the k-th difference of two squared primes.

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Mathematica

A204917 Least j such that n divides s(k)-s(j) for some k>j, where s(j)=(prime(j))^2.

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Mathematica

A204918 Least prime p^2 such that n divides p^2-q^2 for some prime q satisfying q

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Mathematica