A217030 -id:A217030 - cp's OEIS frontend

A217335 Semiprimes p such that next semiprime after p is p+20.

2681, 3523, 6953, 8227, 16817, 26101, 28533, 28563, 28617, 29011, 34249, 37007, 42401, 49983, 50117, 55703, 60657, 65083, 66938, 71381, 71873, 73443, 76247, 92773, 92978, 101109, 101271, 109129, 111479, 112051, 113018, 113721, 115586, 116267, 119969, 124177

Offset: 1

Zak Seidov, Oct 01 2012

nonn

			2681 = A001358(760)  = 7*383, 2701 = A001358(761) = 37*73,
3523 = A001358(986)  = 13*271, 3543 = A001358(987) = 3*1181.

Zak Seidov, Table of n, a(n) for n = 1..2000

Cf. A001358, A065516, A217030.

IsSemiprime:=func; [n: n in [4..130000] | IsSemiprime(n) and IsSemiprime(n+20) and forall{n+i: i in [1..19] | not IsSemiprime(n+i)}]; // Bruno Berselli, Oct 01 2012

f = Flatten@Position[Differences@(s = Select[Range@100000, PrimeOmega@# == 2 &]), 20]; s[[f]] (* Hans Rudolf Widmer, Aug 19 2024 *)

A217357 Semiprimes p such that next semiprime after p is p+30.

Original entry on oeis.org

32777, 88649, 91799, 113107, 165697, 273257, 310103, 322211, 326137, 460963, 466063, 468877, 480443, 483223, 506509, 509131, 553349, 564347, 565493, 587611, 616771, 623257, 624959, 625619, 739177, 766799, 777163, 826657, 832357, 834123, 845177, 860873, 916163

Offset: 1

Zak Seidov, Oct 01 2012

nonn

Smallest difference between two consecutive terms occurs first at a(329) = 5861197 because a(330) = 5861227 and 5861227 - 5861197 = 30. Same difference for a(1212) = 16179703, a(1630) = 20611897 and a(1641) = 20703923.- Zak Seidov, Feb 14 2017

			32777 =A001358(8112)  = 73*449, 32807 = A001358(8113) = 3*619,
88649 =A001358(20880)  = 11*8059, 88679 = A001358(20881) = 71*1249.

Zak Seidov, Table of n, a(n) for n = 1..1000

Cf. A001358, A065516, A217030, A217335.

IsSemiprime:=func; [n: n in [4..1000000] | IsSemiprime(n) and IsSemiprime(n+30) and forall{n+i: i in [1..29] | not IsSemiprime(n+i)}]; // Bruno Berselli, Oct 01 2012

Select[Partition[Select[Range[10^6],PrimeOmega[#]==2&],2,1],#[[2]]-#[[1]] == 30&][[All,1]] (* Harvey P. Dale, May 06 2022 *)

A282407 Semiprimes p such that next semiprime after p is p + 40.

Original entry on oeis.org

741841, 1633213, 1889467, 1946677, 2210557, 2440203, 2655427, 2660857, 2729091, 2749273, 2774911, 3077323, 3724909, 3977473, 4021507, 4030891, 4323301, 4372337, 4408581, 4421713, 4608574, 4640419, 4836223, 5640861, 5691531, 6148599, 6166101, 6429853, 6786523

Offset: 1

Zak Seidov, Feb 14 2017

nonn

Note that a(1) = 741841 = A131109(40).

Smallest difference between two consecutive terms occurs first at a(22060) = 1141901643 because a(22061) = 1141901683 = 1141901643 + 40.

Zak Seidov, Table of n, a(n) for n = 1..23671

Cf. A001358, A131109, A217030, A217335, A217357.

is(p) = if(bigomega(p)==2 && bigomega(p+40)==2, for(i=p+1, p+39, if(bigomega(i)==2, return(0))); 1); \\ Jinyuan Wang, May 23 2021

A282424 Semiprimes p such that next semiprime after p is p + 50.

Original entry on oeis.org

1226777, 4732631, 5093729, 9210671, 12515461, 12917989, 16121409, 16183253, 16698881, 17263069, 19418903, 23003807, 24534161, 26519563, 26726659, 27625067, 29605299, 29772471, 32655031, 34027277, 34366179, 35340719, 37570683, 38117319, 38687461, 39038399, 39479381

Offset: 1

Zak Seidov, Feb 14 2017

nonn

All terms are odd because even semiprime 2*p plus 50 = 2*(p+25) is multiple of 4 and not semiprime.
Note that a(1) = 1226777 = A131109(50).
Smallest possible difference is 50 but among first 10000 terms
the least difference 100 is between a(325) = 228601303 and a(326) = 228601403.

Zak Seidov, Table of n, a(n) for n = 1..10000

Cf. A001358, A131109, A217030, A217335, A217357, A282407.

lista(nn) = my(r); for(k=1, nn, if(bigomega(k)==2, if(k-r==50, print1(r, ", ")); r=k)); \\ Jinyuan Wang, May 23 2021

A133597 Array of semiprimes, read by antidiagonals, where row k is the first of pairs of consecutive semiprimes j and j+k.

Original entry on oeis.org

9, 4, 14, 6, 49, 21, 10, 22, 55, 25, 69, 51, 35, 91, 33, 15, 77, 58, 46, 119, 34, 26, 123, 106, 65, 62, 143, 38, 169, 39, 365, 161, 87, 74, 159, 57, 146, 437, 134, 371, 178, 111, 82, 183, 85, 237, 226, 458, 187, 505, 221, 129, 115, 185, 86

Offset: 1

Jonathan Vos Post, Dec 27 2007

Every semiprime occurs in this table exactly once. Note that similar tables exist for k-almost primes (integers with exactly k prime factors, with multiplicity), this being the k=2 slice of a 3-dimensional array.

			The array begins:
==================================================================
n=......1....2.....3....4....5....6....7....8....9...10
==================================================================
k=1.|...9...14....21...25...33...34...38...57...85...86....A070552
k=2.|...4...49....55...91..119..143..159..183..185..203....A136196
k=3.|...6...22....35...46...62...74...82..115..155..166....A264043
k=4.|. 10...51....58...65...87..111..129..209..249..274....A264044
k=5.|..69...77...106..161..178..221..254..309..314..329....A264045
k=6.|..15..123...365..371..505..545..573..591..649..707....A264046
k=7.|..26...39...134..187..194..267..519..566..655..771....
k=8.|.169..437...458..614..723..737..905..965.1047.1059....
k=9.|.146..226...278..346.1018.1177.1273.1546.1594.1865....
k=10|.237..427..1027.1101.1661.2723.2747.3173.3295.3669....A217030
==================================================================

Cf. A001358, A070552, A136196.

v = Select[Range[5000], PrimeOmega[#]==2 &]; L[k_] := L[k] = v[[Select[Range[Length[v]-1], v[[#+1]] - v[[#]] == k &]]]; Flatten@ Table[ Table[L[k-j+1][[j]], {j, k}], {k, 10}] (* Giovanni Resta, Jun 20 2016 *)

Corrected and edited by Giovanni Resta, Jun 20 2016

cp's OEIS Frontend

A217335 Semiprimes p such that next semiprime after p is p+20.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Magma

Mathematica

A217357 Semiprimes p such that next semiprime after p is p+30.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Magma

Mathematica

A282407 Semiprimes p such that next semiprime after p is p + 40.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI

A282424 Semiprimes p such that next semiprime after p is p + 50.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI

A133597 Array of semiprimes, read by antidiagonals, where row k is the first of pairs of consecutive semiprimes j and j+k.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

Extensions