A176983 -id:A176983 - cp's OEIS frontend

A177829 Positions of 2 in A176983.

2, 28, 47, 49, 135, 173, 225, 258, 375, 384, 439, 507, 525, 545, 552, 570, 577, 583, 600, 629, 665, 691, 784, 818, 855, 886, 1024, 1050, 1076, 1095, 1187, 1245, 1259, 1306, 1367, 1448, 1495, 1501, 1614, 1618, 1646, 1655, 1720, 1812, 1826, 1832, 1843, 1861

Offset: 1

Zak Seidov, May 14 2010

nonn

Cf. A176983, A177829.

A176983(A177829(n))=2.

A177828 First differences of A176983.

Original entry on oeis.org

3, 2, 6, 4, 20, 10, 20, 6, 24, 6, 34, 26, 4, 26, 40, 44, 4, 12, 14, 6, 4, 30, 26, 16, 32, 18, 22, 2, 24, 12, 4, 44, 24, 6, 16, 14, 6, 48, 16, 14, 10, 38, 4, 26, 18, 34, 2, 4, 2, 24, 30, 70, 14, 16, 14, 34, 56, 22, 8, 6, 58, 50, 6, 84, 46, 56, 16, 8, 12, 52, 12, 20, 70, 8, 6, 10, 32, 54

Offset: 1

Zak Seidov, May 14 2010

nonn

a(n)=2 for n=2,28,47,49,135,173,225,258,375,384,439, A177829.

Cf. A176983, A177829.

A177830 Values of k in A176983.

Original entry on oeis.org

1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 4, 4, 4, 6, 2, 2, 4, 2, 2, 4, 2, 2, 2, 2, 6, 2, 4, 4, 4, 2, 4, 2, 4, 2, 2, 6, 2, 2, 2, 2, 2, 2, 4, 2, 4, 2, 2, 4, 4, 2, 4, 2, 2, 4, 2, 4, 4, 2, 2, 2, 4, 2, 2, 4, 2, 2, 4, 4, 2, 2, 4, 2, 2, 2, 2, 6, 4, 2, 4, 2, 2, 2, 2, 4, 2, 4, 2, 2, 2, 2, 2

Offset: 1

Zak Seidov, May 14 2010

nonn

All terms except the first are even.

Cf. A176983.

a(n)=sqrt(nextprime((A176983(n))^2)-(A176983(n))^2)

A177831 Values of q in A176983.

Original entry on oeis.org

5, 29, 53, 173, 293, 1373, 2213, 4493, 5333, 9413, 10613, 18773, 26573, 27893, 37253, 54293, 76733, 78977, 85853, 94253, 97973, 100493, 120413, 139133, 151337, 177257, 192737, 212557, 214373, 237173, 249017, 253013, 299213, 326057, 332933, 351653

Offset: 1

Zak Seidov, May 14 2010

nonn

Includes all terms of A045637 beyond the first, since unless 3 | p either p^2 + 2 or p^2 + 4 must be divisible by 3.

Cf. A045637, A176983.

a(n) = nextprime(A176983(n)^2).

A062324 Primes p such that p^2 + 4 is also prime.

Original entry on oeis.org

3, 5, 7, 13, 17, 37, 47, 67, 73, 97, 103, 137, 163, 167, 193, 233, 277, 293, 307, 313, 317, 347, 373, 463, 487, 503, 547, 577, 593, 607, 613, 677, 743, 787, 823, 827, 853, 883, 953, 967, 983, 997, 1087, 1117, 1123, 1237, 1367, 1423, 1447, 1523, 1543, 1613

Offset: 1

Reiner Martin, Jul 12 2001

Equivalent to the definition: largest absolute dimension of Gaussian primes with prime coordinates. As 2 is the only even prime, the only possibility for a Gaussian prime to have prime coordinates is to be of the form +/-2 +/- I*p or +/-p +/-2*I with p^2+4 a prime, i.e., p is a member of this sequence. - Olivier Gérard, Aug 17 2013
When p > 3, p^2 + 2 is never prime. - Zak Seidov, Nov 04 2013
For p > 5 and q = p^2 + 4, the following congruences apply: q == 3 (mod 10) and q == 5 (mod 12). - Joseph Wheat, Feb 28 2025

			a(1) = 3 because 3^2 + 4 = 13 is prime,
a(4) = 13 because 13^2 + 4 = 173 is prime. - _Zak Seidov_, Nov 04 2013

Harry J. Smith, Table of n, a(n) for n = 1..1000
Yang Ji, Several special cases of a square problem, arXiv:2105.05250 [math.GM], 2021.

The corresponding primes p^2+4 are in A045637.

Subsequence of A176983.

Select[Prime/@Range[300], PrimeQ[ #^2+4]&]

{ n=0; forprime (p=2, 5*10^5, if (isprime(p^2 + 4), write("b062324.txt", n++, " ", p); if (n==1000, break)) ) } \\ Harry J. Smith, Aug 04 2009

a(n) = sqrt(A045637(n) - 4). - Zak Seidov, Nov 04 2013

More terms from Larry Reeves (larryr(AT)acm.org), Jul 20 2001

Edited by Dean Hickerson, Dec 10 2002

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A177829 Positions of 2 in A176983.

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A177828 First differences of A176983.

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A177830 Values of k in A176983.

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A177831 Values of q in A176983.

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A062324 Primes p such that p^2 + 4 is also prime.

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