A062090 -id:A062090 - cp's OEIS frontend

A165285 Primes which are the sum of at least 2 consecutive pars "Prime and PreviousNumber".

17, 43, 59, 73, 79, 101, 109, 139, 163, 191, 197, 233, 239, 283, 317, 331, 379, 419, 433, 439, 443, 463, 467, 499, 521, 569, 571, 599, 617, 619, 641, 739, 743, 787, 811, 863, 911, 919, 941, 967, 971, 1021, 1039, 1061, 1063, 1087, 1097, 1109, 1117, 1229, 1289

Offset: 1

Vladimir Joseph Stephan Orlovsky, Sep 13 2009

(1+2)+(2+3)+(4+5)=17, (4+5)+(6+7)+(10+11)=43, (6+7)+(10+11)+(12+13)=59,..

Cf. A130097, A062090, A050150, A015919

lst={};Do[s=2*Prime[m]-1;Do[p=Prime[n];s+=(2*p-1);If[PrimeQ[s],If[s<=6793,AppendTo[lst,s]]],{n,m+1,3*5!}],{m,1,3*5!}];lst=Take[Union@lst,200]

A326581 Odd integers which are prime or square.

Original entry on oeis.org

1, 3, 5, 7, 9, 11, 13, 17, 19, 23, 25, 29, 31, 37, 41, 43, 47, 49, 53, 59, 61, 67, 71, 73, 79, 81, 83, 89, 97, 101, 103, 107, 109, 113, 121, 127, 131, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 211, 223, 225, 227, 229, 233, 239, 241

Offset: 1

Peter Luschny, Jul 15 2019

nonn

Contains for example 729=27^2 and hence differs from A062090. - R. J. Mathar, Jul 08 2025

Cf. A065091, A000040, A016754, A000290, A326583.

s := n -> if irem(n, 2) = 1 and (isprime(n) or issqr(n)) then n else NULL fi:
seq(s(n), n=0..241);

Select[Range[1, 241, 2], Or[IntegerQ@ Sqrt@ #, PrimeQ@ #] &] (* Michael De Vlieger, Jul 15 2019 *)

Union of A065091 and A016754.

A155187 Prime numbers q of primitive Pythagorean triangles such that perimeters are averages of twin prime pairs, p+1=q(prime), a=q^2-p^2, c=q^2+p^2, b=2pq, ar=a*b/2; s=a+b+c, s-+1 are primes.

Original entry on oeis.org

2, 3, 11, 71, 227, 491, 683, 1103, 1187, 2591, 3923, 4271, 4931, 6737, 7193, 7703, 8093, 8753, 8963, 9173, 9377, 10271, 13043, 13451, 13997, 15233, 15443, 15803, 15887, 17957, 18701, 19961, 20681, 21701, 22031, 22073, 24371, 24473, 24683

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jan 21 2009

nonn

p=1, q=2(prime), a=3, b=4, c=5, s=12-+1 primes, ...

Cf. A020882, A020886, A020884, A020883, A024364, A024406, A155171, A155173, A155174, A155175, A155176, A155177, A155178, A155180, A088483, A001844, A096891, A066885, A099776, A110494, A081589, A155185, A019389, A062090, A050150, A155186, A068231, A129517, A054574, A132281.

lst={};Do[p=n;q=p+1;a=q^2-p^2;c=q^2+p^2;b=2*p*q;ar=a*b/2;s=a+b+c;If[PrimeQ[s-1]&&PrimeQ[s+1],If[PrimeQ[q],AppendTo[lst,q]]],{n,8!}];lst

cp's OEIS Frontend

A165285 Primes which are the sum of at least 2 consecutive pars "Prime and PreviousNumber".

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A326581 Odd integers which are prime or square.

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A155187 Prime numbers q of primitive Pythagorean triangles such that perimeters are averages of twin prime pairs, p+1=q(prime), a=q^2-p^2, c=q^2+p^2, b=2pq, ar=a*b/2; s=a+b+c, s-+1 are primes.

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cp's OEIS Frontend

A165285 Primes which are the sum of at least 2 consecutive pars "Prime and PreviousNumber".

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

A326581 Odd integers which are prime or square.

Views

Author

Keywords

Comments

Crossrefs

Programs

Maple

Mathematica

Formula

A155187 Prime numbers q of primitive Pythagorean triangles such that perimeters are averages of twin prime pairs, p+1=q(prime), a=q^2-p^2, c=q^2+p^2, b=2*p*q, ar=a*b/2; s=a+b+c, s-+1 are primes.

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Programs

Mathematica

A155187 Prime numbers q of primitive Pythagorean triangles such that perimeters are averages of twin prime pairs, p+1=q(prime), a=q^2-p^2, c=q^2+p^2, b=2pq, ar=a*b/2; s=a+b+c, s-+1 are primes.