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A278022 Squares s such that s + 2 and s - 2 are semiprime. 2
36, 121, 144, 289, 1764, 2304, 2601, 2809, 4225, 5184, 5329, 6241, 6889, 7056, 8100, 9409, 13225, 15625, 17689, 19881, 23409, 25281, 27225, 30276, 34969, 35721, 38025, 40401, 41616, 42849, 43681, 45369, 63001, 69696, 72361, 78961, 82369, 84681, 87025, 93636, 106929 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Intersection of A000290 and A105571.

LINKS

K. D. Bajpai, Table of n, a(n) for n = 1..5200

EXAMPLE

a(1) = 36 appears in the list because 36 = 6^2 (square) and 36 + 2 = 38 = 19*2; 36 - 2 = 34 = 17*2; both are semiprime.

a(2) = 121 appears in the list because 121 = 11^2 (square) and 121 + 2 = 123 = 41*3;121 - 2 = 119 = 17*7; both are semiprime.

MATHEMATICA

Select[Table[n^2, {n, 1000}], PrimeOmega[# + 2] == 2 &&  PrimeOmega[# - 2] == 2 &]

Select[Range[350]^2, PrimeOmega[#+{2, -2}]=={2, 2}&] (* Harvey P. Dale, Jun 14 2021 *)

PROG

(PARI) for(n = 1, 1000, s = n^2; if( bigomega(s+2)==2 && bigomega(s-2)==2, print1(s, ", ")))

CROSSREFS

Cf. A000290, A001358, A105571.

Sequence in context: A173420 A271736 A280886 * A333007 A016862 A223506

Adjacent sequences:  A278019 A278020 A278021 * A278023 A278024 A278025

KEYWORD

nonn

AUTHOR

K. D. Bajpai, Nov 08 2016

STATUS

approved

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Last modified November 28 23:48 EST 2021. Contains 349415 sequences. (Running on oeis4.)