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A227129 Semiprimes n = p*q, p<q, such that both numbers n + p - 1 and n + q - 1 are prime. 3
15, 51, 85, 91, 133, 145, 235, 249, 265, 427, 451, 493, 519, 559, 565, 589, 591, 681, 721, 871, 879, 1003, 1149, 1177, 1189, 1207, 1411, 1441, 1509, 1561, 1603, 1651, 1837, 1945, 2059, 2071, 2119, 2227, 2335, 2391, 2419, 2599, 2661, 2827, 2869, 2965, 2995 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Subsequence of A006881.

LINKS

Peter J. C. Moses, Table of n, a(n) for n = 1..5000

Since 591 = 3*197 and numbers 591 + 3 - 1 = 593, 591 + 197 - 1 = 787 are both primes, then 591 is in the sequence.

FORMULA

A226770(a(n)-1) = 2.

MATHEMATICA

Select[Range[10000], (Last[#2]=={1, 1}&&And@@PrimeQ[#1+First[#2]-1]&)[#1, Transpose[FactorInteger[#1]]]&] (* Peter J. C. Moses, Jul 03 2013 *)

spQ[n_]:=Module[{fi=Transpose[FactorInteger[n]]}, fi[[2]]=={1, 1}&&AllTrue[ n-1+fi[[1]], PrimeQ]]; Select[Range[3000], spQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Sep 24 2015 *)

CROSSREFS

Cf. A006881, A226770.

Sequence in context: A075928 A020214 A127643 * A238574 A238575 A020144

Adjacent sequences:  A227126 A227127 A227128 * A227130 A227131 A227132

KEYWORD

nonn

AUTHOR

Vladimir Shevelev, Jul 02 2013

STATUS

approved

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Last modified October 17 13:57 EDT 2019. Contains 328113 sequences. (Running on oeis4.)