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 1-10 of 13 results. Next

A046972 Primes arising in A046966.

Original entry on oeis.org

2, 3, 7, 31, 181, 1621, 19441, 311041, 6842881, 171072001, 4961088001, 153793728001, 5382780480001, 252990682560001, 14420468905920001, 879648603261120001, 58056807815233920001, 4586487817403479680001, 371505513209681854080001, 40122595426645640240640001
Offset: 1

Views

Author

G. L. Honaker, Jr.

Keywords

Links

Crossrefs

Cf. A046966.
Cf. A144717, A144718, A144722, A144723, A144724, A144725, A144726, A144727, A144728, A144729, A144730, A144731. [Artur Jasinski, Sep 19 2008]

Programs

  • Mathematica
    k = 1; a = {}; Do[If[PrimeQ[k n + 1], k = k n; AppendTo[a, k + 1]], {n, 1, 1000}]; a (* Artur Jasinski, Sep 19 2008 *)

A144729 Primes arising in A144728.

Original entry on oeis.org

7, 13, 37, 181, 1621, 19441, 311041, 6842881, 171072001, 4961088001, 153793728001, 5382780480001, 252990682560001, 14420468905920001, 879648603261120001, 58056807815233920001, 4586487817403479680001
Offset: 1

Views

Author

Artur Jasinski, Sep 19 2008; corrected Sep 19 2008

Keywords

Crossrefs

A046966, A046972, A144717, A144718, A144722, A144723, A144724, A144725, A144726, A144727, A144728, A144729, A144730, A144731

A144717 a(n) = smallest positive integer > a(n-1) such that 2*a(1)*a(2)*...*a(n) + 1 is prime.

Original entry on oeis.org

1, 2, 3, 5, 7, 8, 9, 11, 12, 14, 17, 20, 24, 30, 34, 44, 72, 85, 86, 92, 115, 122, 125, 132, 142, 150, 161, 162, 181, 186, 198, 224, 248, 252, 282, 283, 290, 307, 319, 321, 344, 350, 376, 445, 476, 567, 623, 676, 682, 704, 741, 749, 786, 803, 806, 893, 1014, 1046
Offset: 1

Views

Author

Artur Jasinski, Sep 19 2008

Keywords

Examples

			a(1)=1 because a(0) is not defined and 2*1 + 1 = 3 is prime;
a(2)=2 because 2*1*2 + 1 = 5 is prime;
a(3)=3 because 2*1*2*3 + 1 = 13 is prime;
a(4) is not 4 because 2*1*2*3*4 + 1 = 49 is not prime, but a(4)=5 works because 2*1*2*3*5 + 1 = 61 is prime.

Links

Crossrefs

Cf. A046966, A046972, A144718, A144722, A144723, A144724, A144725, A144726, A144727, A144728, A144729, A144730, A144731.

Programs

  • Mathematica
    k = 2; a = {}; Do[If[PrimeQ[k n + 1], k = k n; AppendTo[a, n]], {n, 1, 3000}]; a (* Artur Jasinski *)
nxt[{p_,a_}]:=Module[{k=a+1},While[!PrimeQ[p*k+1],k++];{p*k,k}]; NestList[ nxt,{2,1},60][[All,2]] (* Harvey P. Dale, Aug 18 2021 *)
  • Python
    from sympy import isprime
from itertools import count, islice
def agen(): # generator of terms
    an, p = 1, 2
    while True:
        yield an
        an = next(k for k in count(an+1) if isprime(p*k+1))
        p *= an
print(list(islice(agen(), 58))) # Michael S. Branicky, Jan 13 2023

Extensions

Edited by N. J. A. Sloane, Sep 21 2017 following suggestions from Richard C. Schroeppel

A144718 a(n) = n-th prime arising A144717.

Original entry on oeis.org

3, 5, 13, 61, 421, 3361, 30241, 332641, 3991681, 55883521, 950019841, 19000396801, 456009523201, 13680285696001, 465129713664001, 20465707401216001, 1473530932887552001, 125250129295441920001, 10771511119408005120001
Offset: 1

Views

Author

Artur Jasinski, Sep 19 2008

Keywords

Links

Crossrefs

Cf. A046966, A046972, A144717, A144718, A144722, A144723, A144724, A144725, A144726, A144727, A144728, A144729, A144730, A144731.

Programs

  • Mathematica
    k = 2; a = {}; Do[If[PrimeQ[k n + 1], AppendTo[a, k n+1 ]; k = k n ], {n, 1, 3000}]; a

Formula

a(n) = 2*Product_{k=1..n} A144717(k) + 1.

A144723 a(n)= primes arising A144722.

Original entry on oeis.org

7, 19, 73, 433, 3457, 72577, 1669249, 43400449, 1302013441, 46872483841, 1734281902081, 67636994181121, 2840753755607041, 153400702802780161, 8743840059758469121, 638300324362368245761, 52978926922076564398081
Offset: 1

Views

Author

Artur Jasinski, Sep 19 2008

Keywords

Crossrefs

A046966, A046972, A144717, A144718, A144722, A144723, A144724, A144725, A144726, A144727, A144728, A144729, A144730, A144731

Programs

  • Mathematica
    k = 3; a = {}; Do[If[PrimeQ[k n + 1], AppendTo[a, k n+1 ]; k = k n ], {n, 1, 3000}]; a (*Artur Jasinski*)

A144724 a(n) is the smallest positive integer such that b * (Product_{k=1..n} a(k)) + 1 is prime, with b = 4.

Original entry on oeis.org

1, 3, 5, 7, 8, 9, 11, 12, 14, 17, 20, 24, 30, 34, 44, 72, 85, 86, 92, 115, 122, 125, 132, 142, 150, 161, 162, 181, 186, 198, 224, 248, 252, 282, 283, 290, 307, 319, 321, 344, 350, 376, 445, 476, 567, 623, 676, 682, 704, 741, 749, 786, 803, 806, 893, 1014, 1046, 1079
Offset: 1

Views

Author

Artur Jasinski, Sep 19 2008

Keywords

Comments

Is this A144717 without the 2? - R. J. Mathar, Jul 24 2023

Examples

			4*1+1=5 is prime => a(1)=1.
4*1*2+1=9 is not prime (omitted).
4*1*3+1=13 is prime => a(2)=3.

Crossrefs

Cf. A046966, A046972, A144717, A144718, A144722, A144723, A144725, A144726, A144727, A144728, A144729, A144730, A144731.

Programs

  • Mathematica
    k = 4; a = {}; Do[If[PrimeQ[k n + 1], k = k n; AppendTo[a, n]], {n, 1, 3000}]; a (* Artur Jasinski *)

Extensions

Definition corrected by Georg Fischer, Jun 18 2021

A144725 Primes arising in A144724.

Original entry on oeis.org

5, 13, 61, 421, 3361, 30241, 332641, 3991681, 55883521, 950019841, 19000396801, 456009523201, 13680285696001, 465129713664001, 20465707401216001, 1473530932887552001, 125250129295441920001
Offset: 1

Views

Author

Artur Jasinski, Sep 19 2008; corrected Sep 19 2008

Keywords

Comments

Is this A144718 without the 3? - R. J. Mathar, Jul 24 2023

Crossrefs

A046966, A046972, A144717, A144718, A144722, A144723, A144724, A144725, A144726, A144727, A144728, A144729, A144730, A144731

A144726 Incorrect duplicate of A046966.

Original entry on oeis.org

2, 3, 5, 7, 10, 12, 14, 15, 19, 21, 26, 29, 30, 39, 41, 56, 62, 77, 96, 105, 112, 113, 115, 121, 136, 145, 159, 168, 188, 236, 240, 258, 281, 305, 324, 362, 376, 422, 521, 588, 639, 643, 652, 695, 698, 737, 770, 776, 784, 806, 807, 809, 818, 959, 1023, 1060, 1071
Offset: 1

Views

Author

Artur Jasinski, Sep 19 2008

Keywords

Comments

Previous name was: a(n) is the smallest integer greater than a(n-1) such that a(1)*a(2)*...*a(n) + 1 is prime.

Crossrefs

Cf. A046966, A046972, A144717, A144718, A144722, A144723, A144724, A144725, A144726, A144727, A144728, A144729, A144730, A144731.

Programs

  • Mathematica
    k = 5; a = {}; Do[If[PrimeQ[k n + 1], k = k n; AppendTo[a, n]], {n, 1, 3000}]; a

A144722 a(n) is the smallest positive integer m such that b * (Product_{k=1..n} a(k)) + 1 is prime, with b = 3.

Original entry on oeis.org

2, 3, 4, 6, 8, 21, 23, 26, 30, 36, 37, 39, 42, 54, 57, 73, 83, 86, 88, 91, 93, 98, 99, 112, 120, 137, 140, 142, 148, 161, 162, 169, 171, 174, 179, 237, 247, 294, 312, 335, 340, 382, 474, 475, 484, 498, 500, 539, 589, 598, 653, 654, 660, 704, 720, 732, 789, 804
Offset: 1

Views

Author

Artur Jasinski, Sep 19 2008

Keywords

Examples

			3*1+1=4 is not prime (omitted).
a(1)=2 because 3*2+1=7 is prime.
a(2)=3 because 3*2*3+1=19 is prime.

Crossrefs

Cf. A046966, A046972, A144717, A144718, A144723, A144724, A144725, A144726, A144727, A144728, A144729, A144730, A144731.

Programs

  • Mathematica
    k = 3; a = {}; Do[If[PrimeQ[k*n + 1], k = k*n; AppendTo[a, n]], {n, 1, 3000}]; a

Extensions

Definition corrected by Georg Fischer, Jun 18 2021

A144728 a(n) is the smallest positive integer such that b * (Product_{k=1..n} a(k)) + 1 is prime, with a(n) > a(n-1) for n >= 2, and b = 6.

Original entry on oeis.org

1, 2, 3, 5, 9, 12, 16, 22, 25, 29, 31, 35, 47, 57, 61, 66, 79, 81, 108, 114, 148, 163, 172, 185, 198, 203, 205, 236, 265, 275, 282, 294, 312, 344, 359, 377, 397, 398, 411, 427, 431, 493, 512, 589, 647, 648, 660, 708, 719, 765, 887, 911, 916, 935, 1062, 1093, 1102
Offset: 1

Views

Author

Artur Jasinski, Sep 19 2008

Keywords

Crossrefs

Cf. A046966, A046972, A144717, A144718, A144722, A144723, A144724, A144725, A144726, A144727, A144729, A144730, A144731.

Programs

  • Mathematica
    k = 6; a = {}; Do[If[PrimeQ[k n + 1], k = k n; AppendTo[a, n]], {n, 1, 3000}]; a

Extensions

Definition corrected by Georg Fischer, Jun 18 2021
Showing 1-10 of 13 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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