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 10 results.

A178468 a(n) = smallest prime > a(n-1) such that a(n)+a(n-1) is multiple of k, a(1)=2, k=101.

Original entry on oeis.org

2, 503, 709, 907, 911, 1109, 2729, 2927, 3739, 4139, 4547, 5351, 5557, 6361, 6971, 7573, 7577, 8179, 10607, 11411, 11617, 12421, 12829, 13229, 14243, 15451, 15859, 16057, 16061, 17471, 19697, 21107, 21313, 21713, 22727, 23531, 26161, 26561
Offset: 1

Views

Author

Zak Seidov, May 28 2010

Keywords

Examples

			2+503=505=5*101, 503+709=1212=12*101, 709+907=1616=16*101.

Links

Crossrefs

Cf. A178429 - A178467 cases k=23(2)99, A175442 - A175451 cases k=3(2)21.

Programs

  • Mathematica
    k=101; a=p=2; s={2}; Do[p=NextPrime[p]; If[Mod[a+p, k]==0, a=p; AppendTo[s, a]], {10000}]; s
sp[n_]:=Module[{p=NextPrime[n]},While[Mod[n+p,101]!=0,p=NextPrime[p]];p]; NestList[sp,2,40] (* Harvey P. Dale, Sep 25 2019 *)

A175442 a(n)>a(n-1), a(n) = smallest prime such that a(n)+a(n-1) is multiple of m, a(1)=2, m=3.

Original entry on oeis.org

2, 7, 11, 13, 17, 19, 23, 31, 41, 43, 47, 61, 71, 73, 83, 97, 101, 103, 107, 109, 113, 127, 131, 139, 149, 151, 167, 181, 191, 193, 197, 199, 227, 229, 233, 241, 251, 271, 281, 283, 293, 307, 311, 313, 317, 331, 347, 349, 353, 367, 383, 397, 401, 409, 419, 421
Offset: 1

Views

Author

Zak Seidov, May 28 2010

Keywords

Crossrefs

Cf. A175451.

Programs

  • Mathematica
    Join[{2},Transpose[Select[Partition[Prime[Range[90]],2,1],Divisible[Total[#],3]&]][[2]]]  (* Harvey P. Dale, Feb 20 2011 *)

A175450 a(n)>a(n-1), a(n) = smallest prime greater than a(n-1) such that a(n)+a(n-1) is multiple of m, a(1)=2, m=19.

Original entry on oeis.org

2, 17, 59, 131, 173, 283, 401, 587, 743, 853, 857, 929, 971, 1423, 1427, 1499, 1579, 1613, 1693, 1879, 1997, 2069, 2111, 2221, 2339, 2411, 2719, 2753, 2833, 3019, 3023, 3209, 3251, 3323, 3517, 3779, 3821, 3931, 4049, 4159, 4201, 4273, 4391, 4463, 4657
Offset: 1

Views

Author

Zak Seidov, May 28 2010

Keywords

Links

Crossrefs

Cf. A175451.

Programs

  • Mathematica
    nxt[n_]:=Module[{k=NextPrime[n]},While[!Divisible[n+k,19],k=NextPrime[ k]]; k]; NestList[nxt,2,50] (* Harvey P. Dale, Mar 12 2014 *)

Extensions

Definition corrected by Harvey P. Dale, Mar 12 2014

A175443 a(1)=2, a(n+1) = smallest prime > a(n) such that a(n+1)+a(n) is multiple of 5.

Original entry on oeis.org

2, 3, 7, 13, 17, 23, 37, 43, 47, 53, 67, 73, 97, 103, 107, 113, 127, 163, 167, 173, 197, 223, 227, 233, 257, 263, 277, 283, 307, 313, 317, 353, 367, 373, 397, 433, 457, 463, 467, 503, 547, 563, 577, 593, 607, 613, 617, 643, 647, 653, 677, 683, 727, 733, 757
Offset: 1

Views

Author

Zak Seidov, May 28 2010

Keywords

Comments

Lexicographically first subsequence of primes such that the sum of any two adjacent terms is a multiple of 5. - Charles R Greathouse IV, Apr 13 2015
For n >= 1, a(2*n) == 3 (mod 10) and a(2*n+1) == 7 (mod 10). - Robert Israel, Apr 13 2015

Links

Crossrefs

Cf. A175451.

Programs

  • Maple
    a[1]:= 2: a[2]:= 3:
for n from 2 to 99 do
for t from a[n]+ (-2*a[n] mod 10) by 10 while not isprime(t) do od:
a[n+1]:= t;
od:
seq(a[n],n=1..100); # Robert Israel, Apr 13 2015
  • Mathematica
    spm5[n_]:=Module[{p=NextPrime[n]},While[!Divisible[n+p,5],p = NextPrime[ p]]; p]; NestList[spm5,2,60] (* Harvey P. Dale, Jan 02 2017 *)
  • PARI
    list(lim)=my(v=List([2])); forprime(p=2,lim,if((v[#v]+p)%5,, listput(v,p))); Vec(v) \\ Charles R Greathouse IV, Apr 13 2015

A175444 a(n)>a(n-1), a(n) = smallest prime such that a(n)+a(n-1) is multiple of m, a(1)=2, m=7.

Original entry on oeis.org

2, 5, 23, 47, 79, 89, 107, 131, 149, 173, 191, 229, 233, 257, 317, 383, 401, 439, 443, 467, 499, 509, 541, 593, 653, 677, 709, 719, 751, 761, 821, 859, 863, 887, 919, 929, 947, 971, 1031, 1069, 1087, 1097, 1129, 1153, 1171, 1181, 1213, 1223, 1283, 1307
Offset: 1

Views

Author

Zak Seidov, May 28 2010

Keywords

Links

Crossrefs

Cf. A175451.

Programs

  • Mathematica
    nxt[n_]:=Module[{sp=NextPrime[n]},While[!Divisible[n+sp,7],sp = NextPrime[ sp]]; sp]; NestList[nxt,2,50] (* Harvey P. Dale, Sep 26 2012 *)

A175445 a(n)>a(n-1), a(n) = smallest prime such that a(n)+a(n-1) is multiple of m, a(1)=2, m=9.

Original entry on oeis.org

2, 7, 11, 43, 47, 61, 83, 97, 101, 151, 173, 223, 227, 241, 263, 277, 281, 313, 317, 331, 353, 367, 389, 421, 443, 457, 461, 547, 569, 601, 641, 673, 677, 691, 821, 853, 857, 907, 911, 997, 1019, 1033, 1091, 1123, 1163, 1213, 1217, 1231, 1289, 1303, 1307
Offset: 1

Views

Author

Zak Seidov, May 28 2010

Keywords

Links

Crossrefs

Cf. A175451.

Programs

  • Mathematica
    nxt[n_]:=Module[{c=NextPrime[n]},While[!Divisible[n+c,9],c= NextPrime[ c]];c]; NestList[nxt,2,60] (* Harvey P. Dale, Feb 18 2012 *)

A175446 a(n)>a(n-1), a(n) = smallest prime such that a(n)+a(n-1) is multiple of m, a(1)=2, m=11.

Original entry on oeis.org

2, 31, 79, 97, 101, 163, 167, 229, 233, 251, 277, 317, 409, 449, 541, 647, 673, 691, 739, 757, 761, 823, 827, 911, 937, 977, 1069, 1087, 1091, 1109, 1201, 1307, 1399, 1439, 1487, 1549, 1553, 1571, 1597, 1637, 1663, 1747, 1861, 1879, 1949, 2011, 2081, 2099
Offset: 1

Views

Author

Zak Seidov, May 28 2010

Keywords

Links

Crossrefs

Cf. A175451.

Programs

  • Mathematica
    sp11[a_]:=Module[{k=NextPrime[a]},While[Mod[a+k,11]!=0,k=NextPrime[k]];k]; NestList[ sp11,2,50] (* Harvey P. Dale, Aug 31 2024 *)

A175447 a(n)>a(n-1), a(n) = smallest prime such that a(n)+a(n-1) is multiple of m, a(1)=2, m=13.

Original entry on oeis.org

2, 11, 41, 89, 197, 271, 353, 401, 431, 479, 509, 557, 587, 661, 691, 739, 743, 947, 977, 1051, 1237, 1259, 1289, 1493, 1523, 1571, 1601, 1753, 1783, 1831, 1861, 1987, 2017, 2039, 2069, 2143, 2251, 2273, 2381, 2663, 2693, 2741, 2797, 2819, 2927, 3001, 3083
Offset: 1

Views

Author

Zak Seidov, May 28 2010

Keywords

Links

Crossrefs

Cf. A175451.

Programs

  • Mathematica
    sp[n_]:=Module[{p=NextPrime[n]},While[!Divisible[p+n,13],p= NextPrime[ p]]; p]; NestList[sp,2,50] (* Harvey P. Dale, Sep 24 2016 *)

A175448 a(n)>a(n-1), a(n) = smallest prime such that a(n)+a(n-1) is multiple of m, a(1)=2, m=15.

Original entry on oeis.org

2, 13, 17, 43, 47, 73, 107, 163, 167, 193, 197, 223, 227, 283, 317, 373, 467, 523, 557, 613, 617, 643, 647, 673, 677, 733, 797, 823, 827, 853, 857, 883, 887, 1033, 1097, 1123, 1187, 1213, 1217, 1303, 1307, 1423, 1427, 1453, 1487, 1543, 1607, 1663, 1667, 1693
Offset: 1

Views

Author

Zak Seidov, May 28 2010

Keywords

Links

Crossrefs

Cf. A175451.

Programs

  • Mathematica
    sp15[n_]:=Module[{p=NextPrime[n]},While[!Divisible[n+p,15],p = NextPrime[ p]]; p]; NestList[sp15,2,50] (* Harvey P. Dale, Jan 22 2016 *)

A175449 a(n)>a(n-1), a(n) = smallest prime such that a(n)+a(n-1) is multiple of m, a(1)=2, m=17.

Original entry on oeis.org

2, 83, 223, 389, 461, 491, 563, 593, 631, 661, 733, 797, 937, 967, 971, 1069, 1277, 1307, 1447, 1511, 1549, 1579, 1583, 1613, 1753, 1783, 1787, 1987, 2161, 2293, 2297, 2531, 2671, 2803, 2909, 2939, 3011, 3041, 3079, 3109, 3181, 3313, 3623, 3823, 3929
Offset: 1

Views

Author

Zak Seidov, May 28 2010

Keywords

Crossrefs

Cf. A175451.
Showing 1-10 of 10 results.

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