A113432 -id:A113432 - cp's OEIS frontend

A111344 Pierpont 4-almost primes: numbers with exactly 4 prime divisors, not necessarily distinct, of the form 2^K*3^L + 1.

513, 13825, 32769, 59050, 110593, 157465, 177148, 186625, 262145, 279937, 497665, 1259713, 1327105, 2097153, 2125765, 2519425, 4718593, 4782970, 5668705, 6718465, 17915905, 18874369, 22674817, 33554433, 38263753, 56623105

Offset: 1

Jonathan Vos Post, Nov 08 2005

nonn

			a(1) = 513 = (2^9)*(3^0)+1 = 3 * 3 * 3 * 19.
a(2) = 13825 = (2^9)*(3^3)+1 = 5 * 5 * 7 * 79.
a(3) = 32769 = (2^15)*(3^0)+1 = 3 * 3 * 11 * 331.
a(4) = 59050 = (2^0)*(3^10)+1 = 2 * 5 * 5 * 1181.
a(10) = 279937 = (2^7)*(3^7)+1 = 7 * 7 * 29 * 197 (lots of sevens).
a(24) = 33554433 = (2^25)*(3^0) = 3 * 11 * 251 * 4051.
a(60) = 31381059610 = (2^0)*(3^22)+1 = 2 * 5 * 5501 * 570461.
a(168) = 16677181699666570 = (2^0)*(3^34)+1 = 2 * 5 * 956353 * 1743831169.

Charles R Greathouse IV, Table of n, a(n) for n = 1..2500
Eric Weisstein's World of Mathematics, Pierpont Prime
Eric Weisstein's World of Mathematics, Almost Prime

Intersection of A014613 and A055600.
A005109 gives the Pierpont primes, which are primes of the form (2^K)*(3^L)+1.
A113432 gives the Pierpont semiprimes, 2-almost primes of the form (2^K)*(3^L)+1.
A112797 gives the Pierpont 3-almost primes, of the form (2^K)*(3^L)+1.
A111345 gives the Pierpont 5-almost primes, of the form (2^K)*(3^L)+1.
A111346 gives the Pierpont 6-almost primes, of the form (2^K)*(3^L)+1.
A113739 gives the Pierpont 7-almost primes, of the form (2^K)*(3^L)+1.
A113740 gives the Pierpont 8-almost primes, of the form (2^K)*(3^L)+1.
A113741 gives the Pierpont 9-almost primes, of the form (2^K)*(3^L)+1.

is(n)=bigomega(n)==4 && n-1 == 2^valuation(n-1,2)*3^valuation(n-1,3) \\ Charles R Greathouse IV, Feb 01 2017

list(lim)=my(v=List(),L=lim\1-1); for(e=0,logint(L,3), my(t=3^e); while(t<=L, if(bigomega(t+1)==4, listput(v, t+1)); t*=2)); Set(v) \\ Charles R Greathouse IV, Feb 01 2017

Extended by Ray Chandler, Nov 08 2005

Name edited by Charles R Greathouse IV, Feb 01 2017

A113739 Pierpont 7-almost primes. 7-almost primes of form (2^K)*(3^L)+1.

Original entry on oeis.org

339738625, 10460353204, 83682825625, 669462604993, 2641807540225, 3761479876609, 7625597484988, 18075490334785, 35184372088833, 481469424205825, 488038239039169, 570630428688385, 1125899906842625

Offset: 1

Jonathan Vos Post, Nov 08 2005

nonn

			a(1) = 339738625 = (2^22)*(3^4)+1 = 5 * 5 * 5 * 17 * 29 * 37 * 149.
a(2) = 10460353204 = (2^0)*(3^21)+1 = 2 * 2 * 7 * 7 * 43 * 547 * 2269.
a(3) = 83682825625 = (2^3)*(3^21)+1 = 5 * 5 * 5 * 5 * 7 * 631 * 30313.
a(4) = 669462604993 = (2^6)*(3^21)+1 = 7 * 13 * 19 * 31 * 67 * 277 * 673.
a(7) = 7625597484988 = (2^0)*(3^27)+1 = 2 * 2 * 7 * 19 * 37 * 19441 * 19927.
a(9) = 35184372088833 = (2^45)*(3^0)+1 = 3 * 3 * 3 * 11 * 19 * 331 * 18837001.
a(13) = 1125899906842625 = (2^50)*(3^0)+1 = 5 * 5 * 5 * 41 * 101 * 8101 * 268501.
a(16) = 5559060566555524 = (2^0)*(3^33)+1 = 2 * 2 * 7 * 67 * 661 * 25411 * 176419.
a(28) = 9223372036854775809 = (2^63)*(3^0)+1 = 3 * 3 * 3 * 19 * 43 * 5419 * 77158673929.

Charles R Greathouse IV, Table of n, a(n) for n = 1..716
Eric Weisstein's World of Mathematics, Pierpont Prime
Eric Weisstein's World of Mathematics, Almost Prime

Intersection of A046308 and A055600.
A005109 gives the Pierpont primes, which are primes of the form (2^K)*(3^L)+1.
A113432 gives the Pierpont semiprimes, 2-almost primes of the form (2^K)*(3^L)+1.
A112797 gives the Pierpont 3-almost primes, of the form (2^K)*(3^L)+1.
A111344 gives the Pierpont 4-almost primes, of the form (2^K)*(3^L)+1.
A111345 gives the Pierpont 5-almost primes, of the form (2^K)*(3^L)+1.
A111346 gives the Pierpont 6-almost primes, of the form (2^K)*(3^L)+1.
A113740 gives the Pierpont 8-almost primes, of the form (2^K)*(3^L)+1.
A113741 gives the Pierpont 9-almost primes, of the form (2^K)*(3^L)+1.

list(lim)=my(v=List(), L=lim\1-1); for(e=0, logint(L, 3), my(t=3^e); while(t<=L, if(bigomega(t+1)==7, listput(v, t+1)); t*=2)); Set(v) \\ Charles R Greathouse IV, Feb 01 2017

a(n) is in this sequence iff there exist nonnegative integers K and L such that Omega((2^K)*(3^L)+1) = 7.

Extended by Ray Chandler, Nov 08 2005

A113740 Pierpont 8-almost primes. 8-almost primes of form (2^K)*(3^L)+1.

Original entry on oeis.org

1999004627104432129, 4052555153018976268, 8754997675608244225, 9606056659007943745, 11832592569282330625, 22769912080611422209, 68309736241834266625, 354577405862133891073, 12449449430074295092225

Offset: 1

Jonathan Vos Post, Nov 08 2005

nonn

			a(1) = 1999004627104432129 = (2^18)*(3^27)+1 = 7 * 13 * 19 * 109 * 127 * 181 * 6949 * 66403.
a(2) = 4052555153018976268 = (2^0)*(3^39)+1 = 2 * 2 * 7 * 79 * 157 * 2887 * 10141 * 398581.
a(3) = 8754997675608244225 = (2^55)*(3^5)+1 = 5 * 5 * 11 * 11 * 1201 * 1229 * 16451 * 119191.
a(4) = 9606056659007943745 = (2^6)*(3^36)+1 = 5 * 13 * 17 * 89 * 109 * 281 * 18793 * 169693.
a(13) = 717897987691852588770250 = (2^0)*(3^50)+1 = 2 * 5 * 5 * 5 * 101 * 1181 * 394201 * 61070817601.
a(29) = 1570042899082081611640534564 = (2^0)*(3^57)+1 = 2 * 2 * 7 * 2851 * 3079 * 53923 * 101917 * 1162320517.

Charles R Greathouse IV, Table of n, a(n) for n = 1..993
Eric Weisstein's World of Mathematics, Pierpont Prime
Eric Weisstein's World of Mathematics, Almost Prime

Intersection of A046310 and A055600.
A005109 gives the Pierpont primes, which are primes of the form (2^K)*(3^L)+1.
A113432 gives the Pierpont semiprimes, 2-almost primes of the form (2^K)*(3^L)+1.
A112797 gives the Pierpont 3-almost primes, of the form (2^K)*(3^L)+1.
A111344 gives the Pierpont 4-almost primes, of the form (2^K)*(3^L)+1.
A111345 gives the Pierpont 5-almost primes, of the form (2^K)*(3^L)+1.
A111346 gives the Pierpont 6-almost primes, of the form (2^K)*(3^L)+1.
A113739 gives the Pierpont 7-almost primes, of the form (2^K)*(3^L)+1.
A113741 gives the Pierpont 9-almost primes, of the form (2^K)*(3^L)+1.

list(lim)=my(v=List(), L=lim\1-1); for(e=0, logint(L, 3), my(t=3^e); while(t<=L, if(bigomega(t+1)==8, listput(v, t+1)); t*=2)); Set(v) \\ Charles R Greathouse IV, Feb 06 2017

a(n) is in this sequence iff there exist nonnegative integers K and L such that Omega((2^K)*(3^L)+1) = 8.

Extended by Ray Chandler, Nov 08 2005

A113741 Pierpont 9-almost primes. 9-almost primes of form (2^K)*(3^L)+1.

Original entry on oeis.org

1601009443167990625, 1897492673384285185, 39346408075296537575425, 46005119909369701466113, 221073919720733357899777, 2153693963075557766310748, 3925770232266214525108225

Offset: 1

Jonathan Vos Post, Nov 08 2005

			a(1) = 1601009443167990625 = (2^5)*(3^35)+1 = 5 * 5 * 5 * 5 * 5 * 7 * 11 * 241 * 27608073601.
a(2) = 1897492673384285185 = (2^10)*(3^32)+1 = 5 * 13 * 13 * 13 * 41 * 41 * 373 * 2357 * 116881.

Charles R Greathouse IV, Table of n, a(n) for n = 1..434
Eric Weisstein's World of Mathematics, Pierpont Prime
Eric Weisstein's World of Mathematics, Almost Prime

Intersection of A046312 and A055600.
A005109 gives the Pierpont primes, which are primes of the form (2^K)*(3^L)+1.
A113432 gives the Pierpont semiprimes, 2-almost primes of the form (2^K)*(3^L)+1.
A112797 gives the Pierpont 3-almost primes, of the form (2^K)*(3^L)+1.
A111344 gives the Pierpont 4-almost primes, of the form (2^K)*(3^L)+1.
A111345 gives the Pierpont 5-almost primes, of the form (2^K)*(3^L)+1.
A111346 gives the Pierpont 6-almost primes, of the form (2^K)*(3^L)+1.
A113739 gives the Pierpont 7-almost primes, of the form (2^K)*(3^L)+1.
A113740 gives the Pierpont 8-almost primes, of the form (2^K)*(3^L)+1.

list(lim)=my(v=List(), L=lim\1-1); for(e=0, logint(L, 3), my(t=3^e); while(t<=L, if(bigomega(t+1)==9, listput(v, t+1)); t*=2)); Set(v) \\ Charles R Greathouse IV, Feb 02 2017

a(n) is in this sequence iff there exist nonnegative integers K and L such that Omega((2^K)*(3^L)+1) = 9.

Extended by Ray Chandler, Nov 08 2005

A111345 Pierpont 5-almost primes. 5-almost primes of form (2^K)*(3^L)+1.

Original entry on oeis.org

4375, 19684, 7077889, 7962625, 34012225, 100663297, 129140164, 452984833, 459165025, 544195585, 644972545, 918330049, 5159780353, 7346640385, 8589934593, 13947137605, 14495514625, 23219011585, 27518828545, 28991029249

Offset: 1

Jonathan Vos Post, Nov 08 2005

			a(1) = 4375 = (2^1)*(3^7)+1 = 5 * 5 * 5 * 5 * 7.
a(2) = 19684 = (2^0)*(3^9)+1 = 2 * 2 * 7 * 19 * 37.
a(3) = 7077889 = (2^18)*(3^3)+1 = 7 * 13 * 13 * 31 * 193 (prime factors each have all odd digits).
a(4) = 7962625 = (2^15)*(3^5)+1 = 5 * 5 * 5 * 11 * 5791 (again, coincidentally, prime factors each have all odd
digits).
a(7) = 129140164 = (2^0)*(3^17)+1 = 2 * 2 * 103 * 307 * 1021.
a(15) = 8589934593 = (2^33)*(3^0)+1 = 3 * 3 * 67 * 683 * 20857.
a(21) = 34359738369 = (2^35)*(3^0)+1 = 3 * 11 * 43 * 281 * 86171.
a(30) = 793437161473 = (2^11)*(3^18)+1 = 11 * 11 * 11 * 43 * 13863281.
a(32) = 847288609444 = (2^0)*(3^25)+1 = 2 * 2 * 61 * 151 * 22996651.
a(47) = 68630377364884 = (2^0)*(3^29)+1 = 2 * 2 * 523 * 6091 * 5385997.
a(48) = 70368744177665 = (2^46)*(3^0)+1 = 5 * 277 * 1013 * 1657 * 30269.
a(81) = 50031545098999708 = (2^0)*(3^35)+1 = 2 * 2 * 61 * 547 * 374857981681.
a(89) = 144115188075855873 = (2^57)*(3^0)+1 = 3 * 3 * 571 * 174763 * 160465489.
a(99) = 450283905890997364 = (2^0)*(3^37)+1 = 2 * 2 * 18427 * 107671 * 56737873.
a(113) = 4611686018427387905 = (2^62)*(3^0)+1 = 5 * 5581 * 8681 * 49477 * 384773.

Eric Weisstein's World of Mathematics, Pierpont Prime
Eric Weisstein's World of Mathematics, Almost Prime

Intersection of A014614 and A055600.
A005109 gives the Pierpont primes, which are primes of the form (2^K)*(3^L)+1.
A113432 gives the Pierpont semiprimes, 2-almost primes of the form (2^K)*(3^L)+1.
A112797 gives the Pierpont 3-almost primes, of the form (2^K)*(3^L)+1.
A111344 gives the Pierpont 4-almost primes, of the form (2^K)*(3^L)+1.
A111346 gives the Pierpont 6-almost primes, of the form (2^K)*(3^L)+1.
A113739 gives the Pierpont 7-almost primes, of the form (2^K)*(3^L)+1.
A113740 gives the Pierpont 8-almost primes, of the form (2^K)*(3^L)+1.
A113741 gives the Pierpont 9-almost primes, of the form (2^K)*(3^L)+1.

list(lim)=my(v=List(), L=lim\1-1); for(e=0, logint(L, 3), my(t=3^e); while(t<=L, if(bigomega(t+1)==5, listput(v, t+1)); t*=2)); Set(v) \\ Charles R Greathouse IV, Feb 01 2017

a(n) is in this sequence iff there exist nonnegative integers K and L such that Omega((2^K)*(3^L)+1) = 5.

Extended by Ray Chandler, Nov 08 2005

A111346 Pierpont 6-almost primes. 6-almost primes of form (2^K)*(3^L)+1.

Original entry on oeis.org

14348908, 134217729, 1073741825, 139314069505, 231928233985, 264479053825, 282429536482, 618475290625, 705277476865, 3570467226625, 4398046511105, 8349416423425, 21134460321793, 35664401793025, 91507169819845

Offset: 1

Jonathan Vos Post, Nov 08 2005

			a(1) = 14348908 = (2^0)*(3^15)+1 = 2 * 2 * 7 * 31 * 61 * 271.
a(2) = 134217729 = (2^27)*(3^0)+1 = 3 * 3 * 3 * 3 * 19 * 87211.
a(3) = 1073741825 = (2^30)*(3^0)+1 = 5 * 5 * 13 * 41 * 61 * 1321.
a(4) = 139314069505 = (2^18)*(3^12)+1 = 5 * 13 * 17 * 61 * 337 * 6133.
a(100) = 151115727451828646838273 = (2^77)*(3^0)+1 = 3 * 43 * 617 * 683 * 78233 * 35532364099.
a(127) = 9671406556917033397649409 = (2^83)*(3^0)+1 = 3 * 499 * 1163 * 2657 * 155377 * 13455809771.
a(153) = 523347633027360537213511522 = (2^0)*(3^56)+1 = 2 * 17 * 113 * 193 * 19489 * 36214795668330833.
a(169) = 2475880078570760549798248449 = (2^91)*(3^0)+1 = 3 * 43 * 2731 * 224771 * 1210483 * 25829691707.

Eric Weisstein's World of Mathematics, Pierpont Prime
Eric Weisstein's World of Mathematics, Almost Prime

Intersection of A046306 and A055600.
A005109 gives the Pierpont primes, which are primes of the form (2^K)*(3^L)+1.
A113432 gives the Pierpont semiprimes, 2-almost primes of the form (2^K)*(3^L)+1.
A112797 gives the Pierpont 3-almost primes, of the form (2^K)*(3^L)+1.
A111344 gives the Pierpont 4-almost primes, of the form (2^K)*(3^L)+1.
A111345 gives the Pierpont 5-almost primes, of the form (2^K)*(3^L)+1.
A113739 gives the Pierpont 7-almost primes, of the form (2^K)*(3^L)+1.
A113740 gives the Pierpont 8-almost primes, of the form (2^K)*(3^L)+1.
A113741 gives the Pierpont 9-almost primes, of the form (2^K)*(3^L)+1.

list(lim)=my(v=List(), L=lim\1-1); for(e=0, logint(L, 3), my(t=3^e); while(t<=L, if(bigomega(t+1)==6, listput(v, t+1)); t*=2)); Set(v) \\ Charles R Greathouse IV, Feb 01 2017

a(n) is in this sequence iff there exist nonnegative integers K and L such that Omega((2^K)*(3^L)+1) = 6.

Extended by Ray Chandler, Nov 08 2005

A112797 Pierpont 3-almost primes. 3-almost primes of form (2^K)*(3^L)+1.

Original entry on oeis.org

28, 244, 325, 385, 730, 1025, 1729, 2188, 5185, 6562, 7777, 16385, 26245, 36865, 46657, 49153, 55297, 82945, 93313, 221185, 354295, 419905, 531442, 559873, 589825, 663553, 708589, 884737, 1119745, 1572865, 1594324, 1889569, 2985985

Offset: 1

Jonathan Vos Post, Nov 08 2005

			a(1) = 28 = (2^0)*(3^3)+1 = 2 * 2 * 7.
a(2) = 244 = (2^0)*(3^5)+1 = 2 * 2 * 61.
a(3) = 325 = (2^2)*(3^4)+1 = 5 * 5 * 13.
a(4) = 385 = (2^7)*(3^1)+1 = 5 * 7 * 11.
a(11) = 7777 = (2^5)*(3^5)+1 = 7 * 11 * 101.
a(115) = 94143178828 = (2^0)*(3^23)+1 = 2 * 2 * 23535794707.
a(119) = 137438953473 = (2^37)*(3^0)+1 = 3 * 1777 * 25781083.
a(196) = 281474976710657 = (2^48)*(3^0)+1 = 193 * 65537 * 22253377.

Eric Weisstein's World of Mathematics, Pierpont Prime
Eric Weisstein's World of Mathematics, Almost Prime

Intersection of A014612 and A055600.
A005109 gives the Pierpont primes, which are primes of the form (2^K)*(3^L)+1.
A113432 gives the Pierpont semiprimes, 2-almost primes of the form (2^K)*(3^L)+1.
A111344 gives the Pierpont 4-almost primes, of the form (2^K)*(3^L)+1.
A111345 gives the Pierpont 5-almost primes, of the form (2^K)*(3^L)+1.
A111346 gives the Pierpont 6-almost primes, of the form (2^K)*(3^L)+1.
A113739 gives the Pierpont 7-almost primes, of the form (2^K)*(3^L)+1.
A113740 gives the Pierpont 8-almost primes, of the form (2^K)*(3^L)+1.
A113741 gives the Pierpont 9-almost primes, of the form (2^K)*(3^L)+1.

Take[Select[2^#[[1]] 3^#[[2]] + 1 & /@ Tuples[Range[0, 20], 2],
PrimeOmega[ #]  ==  3 &] // Union, 40] (* Harvey P. Dale, Jan 02 2021 *)

list(lim)=my(v=List(), L=lim\1-1); for(e=0, logint(L, 3), my(t=3^e); while(t<=L, if(bigomega(t+1)==3, listput(v, t+1)); t*=2)); Set(v) \\ Charles R Greathouse IV, Feb 01 2017

a(n) is in this sequence iff there exist nonnegative integers K and L such that Omega((2^K)*(3^L)+1) = 3.

Extended by Ray Chandler, Nov 08 2005

A113433 Semi-Pierpont semiprimes: products of exactly two Pierpont primes A005109.

Original entry on oeis.org

4, 6, 9, 10, 14, 15, 21, 25, 26, 34, 35, 38, 39, 49, 51, 57, 65, 74, 85, 91, 95, 111, 119, 133, 146, 169, 185, 194, 218, 219, 221, 247, 259, 289, 291, 323, 326, 327, 361, 365, 386, 481, 485, 489, 511, 514, 545, 579, 629, 679, 703, 763, 771, 815, 866, 949, 965

Offset: 1

Jonathan Vos Post, Nov 01 2005

Semiprime both of whose prime factors are Pierpont primes (A005109), which are primes of the form (2^K)*(3^L)+1. Not to be confused with A113432: Pierpont semiprimes [Semiprimes of the form (2^K)*(3^L)+1]. This terminology itself is by analogy to what Tomaszewski used for the Sophie Germain counterparts A111153 and A111206.

			a(1) = 4 = 2^2 = [(2^0)*(3^0)+1]*[(2^1)*(3^0)+1] = A005109(1)*A005109(1).
a(2) = 6 = 2*3 = [(2^0)*(3^0)+1]*[(2^1)*(3^0)+1] = A005109(1)*A005109(2).
a(3) = 9 = 3^2 = [(2^1)*(3^0)+1]*[(2^1)*(3^0)+1] = A005109(2)*A005109(2).
a(4) = 10 = 2*5 = [(2^0)*(3^0)+1]*[(2^2)*(3^0)+1] = A005109(1)*A005109(3).
a(5) = 14 = 2*7 = [(2^0)*(3^0)+1]*[(2^1)*(3^1)+1] = A005109(1)*A005109(4).
a(6) = 15 = 3*5 = [(2^1)*(3^0)+1]*[(2^2)*(3^0)+1] = A005109(2)*A005109(3).

Vincenzo Librandi, Table of n, a(n) for n = 1..498
Chris Caldwell, "Pierpont primes." primeform posting, Oct 25, 2005.
Chris Caldwell, "Pierpont primes." primeform posting, Oct 25, 2005. [Cached copy]
Eric Weisstein's World of Mathematics, Pierpont Prime
Eric Weisstein's World of Mathematics, Semiprime

Cf. A001358, A003586, A005109, A055600, A111153, A111206, A113432, A113434.

Select[Range[10^3], Plus @@ Last /@ FactorInteger[ # ] == 2 && And @@ (Max @@ First /@ FactorInteger[ # - 1] < 5 &) /@ First /@ FactorInteger[ # ] &] (* Ray Chandler, Jan 24 2006 *)

{a(n)} = Semiprimes A001358 both of whose factors are of the form (2^K)*(3^L)+1. {a(n)} = {A005109(i)*A005109(j) for integers i and j not necessarily distinct}.

A113434 Semi-Pierpont semiprimes which are also Pierpont semiprimes.

Original entry on oeis.org

4, 9, 10, 25, 49, 65, 289

Offset: 1

Jonathan Vos Post, Nov 01 2005

Semiprimes both of whose prime factors are Pierpont primes (A005109), which are primes of the form (2^K)*(3^L)+1 and where the semiprime is itself of the form (2^K)*(3^L)+1.
No more under 10^50; what is the next element of this sequence?
No more terms <= 10^100. - Robert Israel, Mar 10 2017
This sequence is complete, see Links. - Charlie Neder, Feb 04 2019

			a(1) = 4 = 2^2 = [(2^0)*(3^0)+1]*[(2^0)*(3^0)+1] = (2^0)*(3^1)+1.
a(2) = 9 = 3^2 = [(2^1)*(3^0)+1]*[(2^1)*(3^0)+1] = (2^3)*(3^0)+1.
a(3) = 10 = 2*5 = [(2^0)*(3^0)+1]*[(2^2)*(3^0)+1] = (2^0)*(3^2)+1.
a(4) = 25 = 5^2 = [(2^2)*(3^0)+1]*[(2^2)*(3^0)+1] = (2^3)*(3^1)+1.
a(5) = 49 = 7^2 = [(2^1)*(3^1)+1]*[(2^1)*(3^1)+1] = (2^4)*(3^1)+1.
a(6) = 65 = 5*13 = [(2^2)*(3^0)+1]*[(2^2)*(3^1)+1] = (2^6)*(3^0)+1.
a(7) = 289 = 17^2 = [(2^4)*(3^0)+1]*[(2^4)*(3^0)+1] = (2^5)*(3^2)+1.

Chris Caldwell, "Pierpont primes." primeform posting, Oct 25, 2005.
Chris Caldwell, "Pierpont primes." primeform posting, Oct 25, 2005. [Cached copy]
Charlie Neder, Proof of the completeness of this sequence
Eric Weisstein's World of Mathematics, Pierpont Prime
Eric Weisstein's World of Mathematics, Semiprime

Cf. A001358, A003586, A005109, A055600, A111153, A111206, A113432, A113433.

N:= 10^100: # to get all terms <= N
PP:= select(isprime, {seq(seq(1+2^i*3^j, i=0..ilog2((N-1)/3^j)),j=0..floor(log[3](N-1)))}):
SP:= select(t -> t <= N and t = 1+2^padic:-ordp(t-1,2)*3^padic:-ordp(t-1,3), [seq(seq(PP[i]*PP[j], j=1..i),i=1..nops(PP))]):
sort(convert(SP,list)); # Robert Israel, Mar 10 2017

{a(n)} = intersection of A113432 and A113433. {a(n)} = Semiprimes A001358 of the form (2^K)*(3^L)+1 both of whose factors are of the form (2^K)*(3^L)+1. {a(n)} = {integers P such that, for nonnegative integers I, J, K, L, m, n there is a solution to (2^I)*(3^J)+1 = [(2^K)*(3^L)+1]*[(2^m)*(3^n)+1] where both [(2^K)*(3^L)+1] and [(2^m)*(3^n)+1] are prime}.

cp's OEIS Frontend

A111344 Pierpont 4-almost primes: numbers with exactly 4 prime divisors, not necessarily distinct, of the form 2^K*3^L + 1.

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A113739 Pierpont 7-almost primes. 7-almost primes of form (2^K)*(3^L)+1.

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A113740 Pierpont 8-almost primes. 8-almost primes of form (2^K)*(3^L)+1.

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A113741 Pierpont 9-almost primes. 9-almost primes of form (2^K)*(3^L)+1.

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A111345 Pierpont 5-almost primes. 5-almost primes of form (2^K)*(3^L)+1.

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A111346 Pierpont 6-almost primes. 6-almost primes of form (2^K)*(3^L)+1.

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A112797 Pierpont 3-almost primes. 3-almost primes of form (2^K)*(3^L)+1.

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A113433 Semi-Pierpont semiprimes: products of exactly two Pierpont primes A005109.