1,1

Prompted by a question from Shiv K. Gupta to the Number Theory mailing list.

D. Broadhurst in reply to S. K. Gupta, Hypotenuses of Integral Right Triangles - again, NMBRTHRY list, Feb 24 2009

a(n) = min { A002144(k) | A145010(k) > A145010(k+1) > ... > A145010(k+n-1)}. - M. F. Hasler (MHasler(AT)univ-ag.fr), Feb 26 2009

Comment from M. F. Hasler (MHasler(AT)univ-ag.fr), Feb 24 2009:

The first sequence of 12 such primes is the one starting at a(12) =

931953301 = [27050, 14151]^2 ; area = 203431499448450450

931953389 = [26050, 15917]^2 ; area = 176325413694076350

931953397 = [25239, 17174]^2 ; area = 148267841956285170

931953409 = [24528, 18175]^2 ; area = 120941067830427600

931953433 = [30332, 3453 ]^2 ; area = 95111855933417940

931953437 = [23846, 19061]^2 ; area = 93319265825216970

931953469 = [30462, 2005 ]^2 ; area = 56429222392003890

931953509 = [30478, 1745 ]^2 ; area = 49241224048436490

931953569 = [30487, 1580 ]^2 ; area = 44651199683914740

931953637 = [22166, 20991]^2 ; area = 23594434443844350

931953709 = [30525 , 422 ]^2 ; area = 12000420304268550

931953733 = [21793, 21378]^2 ; area = 8346882442487610

(PARI) A144954( n, p=5, verbose=0, L=[0])={ for( i=1, n-1, while(( p=nextprime(p+2)) % 4 !=1, ); mn=sum2sqr_prime(p); L=if( L[i] > A=mn[1]*mn[2]*abs(mn[1]^2-mn[2]^2), concat( L, A), i=0; [A]) ); for( i=0, n-1, i & while( 1 != (p=precprime(p-2)) % 4, ); verbose & print( p" = " sum2sqr_prime(p) "^2 ; area = " L[n-i])); p} - M. F. Hasler (MHasler(AT)univ-ag.fr), Feb 24 2009

Cf. A145010, A002144, A002330, A002331. See A144960 for the actual primes.

Sequence in context: A089195 A023289 A006468 this_sequence A146195 A095924 A088582

Adjacent sequences: A144951 A144952 A144953 this_sequence A144955 A144956 A144957

nonn

David Broadhurst, Feb 24 2009