A232878 -id:A232878 - cp's OEIS frontend

A069496 Smaller member of a twin prime pair with a square sum.

17, 71, 881, 1151, 2591, 3527, 4049, 15137, 20807, 34847, 46817, 69191, 83231, 103967, 112337, 149057, 176417, 179999, 206081, 281249, 362951, 388961, 438047, 472391, 478241, 538721, 649799, 734471, 808991, 960497, 1080449, 1143071

Offset: 1

Amarnath Murthy, Mar 30 2002

nonn

All members of this sequence have digital root 8. - J. W. Helkenberg, Jul 24 2013

First bisection of A232878. - Gary Croft, Dec 05 2013

			71 is a term as the smaller member of the twin prime pair (71,73) as 71+73 = 144 = 12^2.

T. D. Noe, Table of n, a(n) for n = 1..10000
Author?, Title? (no longer exists)

Cf. A118593, A232878.

isa := n -> isprime(n) and isprime(n+2) and issqr(2*n+2):
select(isa, [$4..1000000]); # Peter Luschny, Jan 05 2020

First/@Select[Partition[Prime[Range[9*10^4]],2,1],Differences[#]=={2} && IntegerQ[Sqrt[Total[#]]] &] (* Jayanta Basu, May 26 2013 *)

t(n, p=3) = {while( p+2 < (p=nextprime( p+1 )) || n-->0, ); p-2}
for(n=1, 1e4, if(issquare(2*t(n)+2), print1(t(n), ", "))); \\ Altug Alkan, Mar 14 2016

a(n) = (A037072(n)-2)/2.

a(n) = A118593(n) - 2. - Zerinvary Lajos, Jul 31 2006

More terms from Sascha Kurz, Apr 01 2002

A235334 Numbers n such that for any positive integers (a, b), if a * b = n then a + b is a square.

Original entry on oeis.org

3, 323, 5183, 777923, 1327103, 6718463, 12446783, 16402499, 229159043, 432972863, 1214383103, 2191925123, 4787532863, 6927565823, 10809345023, 12619826243, 22218287363, 31123310723, 32399999999, 42469790723, 79101562499, 131734154303, 151291437443

Offset: 1

Michel Lagneau, Jan 06 2014

nonn

It seems that n is the product of twin primes of A232878 for n > 3.

Conjecture: the numbers n such that for any positive integers (a, b), a * b = n and a + b is a square are the product of twin primes, and a*b+1 is also a perfect square.

			323 is the product of two positive integers in 2 ways: 1 * 323 and 17 * 19. The sums of the pairs of multiplicands are 323+1 = 18^2 and 17+19 = 6^2 respectively. All are squares.

Hiroaki Yamanouchi, Table of n, a(n) for n = 1..1163

Cf. A001097, A080715, A232878.

t={}; Do[ds=Divisors[n]; If[EvenQ[Length[ds]], ok=True; k=1; While[k<=Length[ds]/2 && (ok=IntegerQ[Sqrt[ds[[k]]+ds[[ -k]]]]), k++ ]; If[ok, AppendTo[t, n]]], {n, 2, 10^8}]; t ***[Program from T.D. Noe adapted for this sequence. See A080715]***

isok(n) = {d = divisors(n); if (#d % 2, return (0)); for (i = 1, #d/2, if (! issquare(d[i]+n/d[i]), return (0));); return (1);} \\ Michel Marcus, Jan 06 2014

a(21)-a(23) from Hiroaki Yamanouchi, Oct 02 2014

cp's OEIS Frontend

A069496 Smaller member of a twin prime pair with a square sum.

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