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A078667 Integers that occur more than once as the difference of the squares of two consecutive primes. 7
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 (list; graph; refs; listen; history; text; internal format)
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 *)

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: A166987 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

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Last modified November 14 17:24 EST 2019. Contains 329126 sequences. (Running on oeis4.)