cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-8 of 8 results.

A157352 Products (semiprimes) of two distinct safe primes.

Original entry on oeis.org

35, 55, 77, 115, 161, 235, 253, 295, 329, 413, 415, 517, 535, 581, 649, 749, 835, 895, 913, 1081, 1135, 1169, 1177, 1253, 1315, 1357, 1589, 1735, 1795, 1837, 1841, 1909, 1915, 1969, 2335, 2395, 2429, 2461, 2497, 2513, 2515, 2681, 2773, 2815, 2893, 2935
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Feb 27 2009

Keywords

Comments

35=5*7; 5 and 7 are safe primes, 55=5*11; 5 and 11 are safe primes,...

Examples

			a(1) = 35 since 35 = 5 * 7, and (5 - 1)/2 = 2 and (7 - 1)/2 = 3 are both prime, thus 5 and 7 are distinct safe primes.

Links

Crossrefs

Cf. A001358, A005384, A005385, A006881, A007304, A111206, A157342, A157344, A157345, A157346, A157347.

Programs

  • Mathematica
    lst={};Do[If[Plus@@Last/@FactorInteger[n]==2,a=Length[First/@FactorInteger[n]];If[a==2,b=First/@FactorInteger[n];c=b[[1]];d=b[[2]];If[PrimeQ[(c-1)/2]&&PrimeQ[(d-1)/2],AppendTo[lst,n]]]],{n,7!}];lst
Select[Select[Range@ 3000, PrimeNu@ # == 2 &], Times @@ Map[If[PrimeQ[(# - 1)/2], #, 0] &, Map[First, FactorInteger@ #]] == # &] (* Michael De Vlieger, Feb 28 2016 *)
Module[{upto=3000,sp},sp=Select[Prime[Range[PrimePi[upto/5]]],PrimeQ[(#-1)/2]&];Select[Union[Times@@@Subsets[sp,{2}]],#<+upto&]] (* Harvey P. Dale, Aug 25 2017 *)

Extensions

Example corrected by Harvey P. Dale, Aug 25 2017

A157346 Products of 3 distinct Sophie Germain primes.

Original entry on oeis.org

30, 66, 110, 138, 165, 174, 230, 246, 290, 318, 345, 410, 435, 498, 506, 530, 534, 615, 638, 678, 759, 786, 795, 830, 890, 902, 957, 1038, 1074, 1130, 1146, 1166, 1245, 1265, 1310, 1334, 1335, 1353, 1398, 1434, 1506, 1595, 1686, 1695, 1730, 1749, 1758, 1790
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Feb 27 2009

Keywords

Examples

			30 = 2*3*5; 2,3 and 5 are distinct Sophie Germain primes.
66 = 2*3*11; 2,3 and 11 are distinct Sophie Germain primes.

Links

Crossrefs

Cf. A001358, A005384, A111206, A157342, A006881, A157344, A157345, A007304.

Programs

  • Mathematica
    lst={};Do[If[Plus@@Last/@FactorInteger[n]==3,a=Length[First/@FactorInteger[n]];If[a==3,b=First/@FactorInteger[n];c=b[[1]];d=b[[2]];e=b[[3]];If[PrimeQ[2*c+1]&&PrimeQ[2*d+1]&&PrimeQ[2*e+1],AppendTo[lst,n]]]],{n,7!}];lst
With[{sgps=Select[Prime[Range[100]],PrimeQ[2#+1]&]},Take[Union[ Times@@@ Subsets[sgps,{3}]],60]] (* Harvey P. Dale, Aug 10 2011 *)

A157347 Products of 3 distinct non-Sophie Germain primes.

Original entry on oeis.org

1547, 1729, 2261, 2821, 3367, 3689, 3913, 4123, 4199, 4277, 4403, 4921, 5117, 5369, 5551, 5593, 5719, 6097, 6251, 6461, 6643, 6851, 7021, 7189, 7259, 7657, 7847, 7973, 8029, 8113, 8177, 8449, 8687, 8827, 8911, 9139, 9191, 9331, 9373, 9401, 9443, 9503
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Feb 27 2009

Keywords

Examples

			1547 = 7*13*17 is a term: its prime factors 7, 13, and 17 are not Sophie Germain primes.

Links

Crossrefs

Cf. A001358, A005384, A111206, A157342, A006881, A157344, A157345, A007304, A157346.

Programs

  • Magma
    S:=[ p: p in PrimesUpTo(120) | not IsPrime(2*p+1) ]; T:=[ q: a, b, c in S | a lt b and b lt c and q lt 10000 where q is a*b*c ]; Sort(~T); T; // Klaus Brockhaus, Apr 11 2009
  • Mathematica
    lst={};Do[If[Plus@@Last/@FactorInteger[n]==3,a=Length[First/@FactorInteger[n]];If[a==3,b=First/@FactorInteger[n];c=b[[1]];d=b[[2]];e=b[[3]];If[ !PrimeQ[2*c+1]&&!PrimeQ[2*d+1]&&!PrimeQ[2*e+1],AppendTo[lst,n]]]],{n,8!}];lst

Extensions

Entries verified by Klaus Brockhaus, Apr 11 2009

A157353 Products (semiprimes) of two distinct primes that are not safe primes.

Original entry on oeis.org

6, 26, 34, 38, 39, 51, 57, 58, 62, 74, 82, 86, 87, 93, 106, 111, 122, 123, 129, 134, 142, 146, 158, 159, 178, 183, 194, 201, 202, 206, 213, 218, 219, 221, 226, 237, 247, 254, 262, 267, 274, 278, 291, 298, 302, 303, 309, 314, 323, 326, 327, 339, 346, 362, 377
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Feb 27 2009

Keywords

Examples

			6=2*3; 2 and 3 are not safe primes.
26=2*13; 2 and 13 are not safe primes.

Crossrefs

Cf. A001358, A005384, A005385, A006881, A007304, A111206, A157342, A157344, A157345, A157346, A157347, A157352.

Programs

  • Mathematica
    lst={};Do[If[Plus@@Last/@FactorInteger[n]==2,a=Length[First/@FactorInteger[n]];If[a==2,b=First/@FactorInteger[n];c=b[[1]];d=b[[2]];If[ !PrimeQ[(c-1)/2]&&!PrimeQ[(d-1)/2],AppendTo[lst,n]]]],{n,7!}];lst

A157354 Products of 3 distinct safe primes.

Original entry on oeis.org

385, 805, 1265, 1645, 1771, 2065, 2585, 2905, 3245, 3619, 3745, 4543, 4565, 5405, 5845, 5885, 6265, 6391, 6785, 7567, 7945, 8239, 9185, 9205, 9499, 9545, 9845, 11891, 12145, 12305, 12485, 12565, 12859, 13363, 13405, 13783, 13865, 14465, 14927
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Feb 27 2009

Keywords

Examples

			385=5*7*11; 5,7 and 11 are safe primes.

Links

Crossrefs

Subsequence of A007304.
Cf. A001358, A005384, A005385, A006881, A111206, A157342, A157344, A157345, A157346, A157347, A157352, A157353

Programs

  • Mathematica
    lst={};Do[If[Plus@@Last/@FactorInteger[n]==3,a=Length[First/@FactorInteger[n]];If[a==3,b=First/@FactorInteger[n];c=b[[1]];d=b[[2]];e=b[[3]];If[PrimeQ[(c-1)/2]&&PrimeQ[(d-1)/2]&&PrimeQ[(e-1)/2],AppendTo[lst,n]]]],{n,7!}];lst
  • PARI
    list(lim)=my(v=List(),P=select(p->isprime(p\2), primes([5,sqrtint(lim\5+1)-1])),p,q,t); for(i=1,#P, p=P[i]; if(p^3>=lim, break); for(j=i+1,#P, q=P[j]; t=p*q; forprime(r=q+4,lim\t, if(isprime(r\2), listput(v,r*t))))); Set(v); \\ Charles R Greathouse IV, Oct 14 2021

A157357 Products of 3 distinct triple-safe primes.

Original entry on oeis.org

777239, 1555559, 3112199, 4409399, 10635959, 12192599, 23348519, 23796743, 30612839, 47610023, 48628127, 55778519, 67454423, 91581239, 95286263, 97290047, 99883319, 102996599, 104812679, 135002663, 137841647, 148398599, 162707543, 170450999, 172007639, 186520823
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Feb 27 2009

Keywords

Examples

			777239=23*47*719; 23, 47, and 719 are triple-safe prime numbers.

Links

Crossrefs

Cf. A157358, A001358, A005384, A005385, A006881, A007304, A066179, A111206, A157342, A157344, A157345, A157346, A157347, A157352, A157353, A157354, A157355, A157356

Programs

  • Mathematica
    lst={};Do[If[Plus@@Last/@FactorInteger[n]==3,a=Length[First/@FactorInteger[n]];If[a==3,b=First/@FactorInteger[n];c=b[[1]];d=b[[2]];e=b[[3]];If[PrimeQ[cx=(c-1)/2]&&PrimeQ[cy=(cx-1)/2]&&PrimeQ[(cy-1)/2]&&PrimeQ[dx=(d-1)/2]&&PrimeQ[dy=(dx-1)/2]&&PrimeQ[(dy-1)/2]&&PrimeQ[ex=(e-1)/2]&&PrimeQ[ey=(ex-1)/2]&&PrimeQ[(ey-1)/2],AppendTo[lst,n]]]],{n,9!,11!}];lst
  • PARI
    list(lim)=my(v=List(), P=select(p->isprime(p\2) && isprime(p\4) && isprime(p\8), primes([11, sqrtint(lim\11+1)-1])), p, q, t); for(i=1, #P, p=P[i]; if(p^3>=lim, break); for(j=i+1, #P, q=P[j]; t=p*q; forprime(r=q+4, lim\t, if(isprime(r\2) && isprime(r\4) && isprime(r\8), listput(v, r*t))))); Set(v); \\ Charles R Greathouse IV, Oct 14 2021

Extensions

a(5)-a(26) from Charles R Greathouse IV, Oct 14 2021

A157355 Products of 3 distinct not safe primes.

Original entry on oeis.org

78, 102, 114, 174, 186, 222, 246, 258, 318, 366, 402, 426, 438, 442, 474, 494, 534, 582, 606, 618, 646, 654, 663, 678, 741, 754, 762, 786, 806, 822, 834, 894, 906, 942, 962, 969, 978, 986, 1038, 1054, 1066, 1086, 1102, 1118, 1131, 1146, 1158, 1178, 1182
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Feb 27 2009

Keywords

Comments

78=2*3*13; 2,3 and 13 are not safe prime numbers,...

Crossrefs

Cf. A001358, A005384, A005385, A006881, A007304, A111206, A157342, A157344, A157345, A157346, A157347, A157352, A157353, A157354

Programs

  • Mathematica
    lst={};Do[If[Plus@@Last/@FactorInteger[n]==3,a=Length[First/@FactorInteger[n]];If[a==3,b=First/@FactorInteger[n];c=b[[1]];d=b[[2]];e=b[[3]];If[ !PrimeQ[(c-1)/2]&&!PrimeQ[(d-1)/2]&&!PrimeQ[(e-1)/2],AppendTo[lst,n]]]],{n,7!}];lst

A157356 Products (semiprimes) of two distinct double-safe primes.

Original entry on oeis.org

253, 517, 1081, 1837, 3841, 3949, 7849, 7909, 8257, 15829, 16537, 16873, 22429, 31669, 33097, 33793, 44869, 45397, 46897, 54109, 59953, 62029, 63877, 65197, 66217, 66517, 67633, 79717, 83149, 83677, 84997, 93817, 94921, 95833, 108229
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Feb 27 2009

Keywords

Comments

253=11*23; 11 and 23 are double safe prime numbers; (11-1)/2=5; (5-1)/2=2(prime); (23-1)/2=11; (11-1)/2=5(prime), ...

Crossrefs

Cf. A001358, A005384, A005385, A006881, A007304, A066179, A111206, A157342, A157344, A157345, A157346, A157347, A157352, A157353, A157354, A157355

Programs

  • Mathematica
    lst={};Do[If[Plus@@Last/@FactorInteger[n]==2,a=Length[First/@FactorInteger[n]];If[a==2,b=First/@FactorInteger[n];c=b[[1]];d=b[[2]];If[PrimeQ[cx=(c-1)/2]&&PrimeQ[(cx-1)/2]&&PrimeQ[dx=(d-1)/2]&&PrimeQ[(dx-1)/2],AppendTo[lst,n]]]],{n,9!}];lst
Showing 1-8 of 8 results.

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