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

72, 120, 168, 312, 408, 552, 600, 768, 792, 912, 1032, 1848, 2472, 3048, 3192, 3288, 3528, 3720, 4008, 4920, 5160, 5208, 5808, 5928, 6072, 6480, 6792, 6840, 6888, 7080, 7152, 7248, 7512, 7728, 7800, 8520, 8760, 9072, 11400, 11880, 11928, 12792, 13200, 13320

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..44.

Example

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

Mathematica

Sort@ DeleteDuplicates@ Flatten@ Select[Gather[NextPrime[#]^2 - #^2 & /@ Prime@ Range@ 1200], Length@ # > 1 &] (* Michael De Vlieger, Mar 18 2015 *)
Select[Tally[Differences[Prime[Range[1000]]^2]], #[[2]]>1&][[;; , 1]]//Sort (* Harvey P. Dale, Nov 16 2023 *)

Prog

(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]", ")))

Crossrefs

Cf. A090783, A090784, A090785, A091878.

Sequence in context: A339940 A251124 A169644 * A090784 A291805 A266345

Adjacent sequences: A078664 A078665 A078666 * A078668 A078669 A078670

Keyword

nonn

Author

Jon Perry, Dec 15 2002

Extensions

Duplicate terms removed, as suggested by Richard R. Forberg, by Jon E. Schoenfield, Mar 15 2015

Status

approved