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

%I #23 Nov 16 2023 11:32:44

%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 *)

%t Select[Tally[Differences[Prime[Range[1000]]^2]],#[[2]]>1&][[;;,1]]//Sort (* _Harvey P. Dale_, Nov 16 2023 *)

%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 March 28 07:20 EDT 2024. Contains 371235 sequences. (Running on oeis4.)