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 A078667 Integers that occur more than once as the difference of the squares of two consecutive primes. 7

%I

%S 72,120,168,312,408,552,600,768,792,912,1032,1848,2472,3048,3192,3288,

%T 3528,3720,4008,4920,5160,5208,5808,5928,6072,6480,6792,6840,6888,

%U 7080,7152,7248,7512,7728,7800,8520,8760,9072,11400,11880,11928,12792,13200,13320

%N Integers that occur more than once as the difference of the squares of two consecutive primes.

%C 1848 is the first integer that occurs exactly three times. The next few are 6888, 14280, 16008, 19152. 4920 is the first integer that occurs exactly four times. See A069482 for more details. - _Richard R. Forberg_, Feb 06 2015

%e 120 = 31^2 - 29^2 = 17^2 - 13^2.

%t Sort@ DeleteDuplicates@ Flatten@ Select[Gather[NextPrime[#]^2 - #^2 & /@ Prime@ Range@ 1200], Length@ # > 1 &] (* _Michael De Vlieger_, Mar 18 2015 *)

%o (PARI) pv(v)=vecsort(vecextract(v,concat("1..",vc-1))) op=2; v=vector(5000); vc=1; forprime (p=3,5000,v[vc]=p^2-op^2; vc++; op=p) v=pv(v) for (i=2,length(v), if (v[i]==v[i-1],print1(v[i]",")))

%Y Cf. A090783, A090784, A090785, A091878.

%K nonn

%O 1,1

%A _Jon Perry_, Dec 15 2002

%E Duplicate terms removed, as suggested by _Richard R. Forberg_, by _Jon E. Schoenfield_, Mar 15 2015

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Last modified September 30 23:44 EDT 2020. Contains 337440 sequences. (Running on oeis4.)