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 1-4 of 4 results.

A175075 Primes q with result 2 under iterations of {r mod (max prime p < r)} starting at r = q.

Original entry on oeis.org

2, 5, 7, 13, 19, 31, 43, 61, 73, 103, 109, 139, 151, 181, 193, 199, 229, 241, 271, 283, 313, 349, 421, 433, 463, 523, 571, 601, 619, 643, 661, 811, 823, 829, 859, 883, 1021, 1033, 1051, 1063, 1093, 1153, 1231, 1279, 1291, 1303, 1321, 1429, 1453, 1483, 1489
Offset: 1

Views

Author

Jaroslav Krizek, Jan 23 2010

Keywords

Comments

a(1) = 2, a(n) = A006512(n-1) for 2 <= n <= 82, a(83) = 2999. Sequence is the union of A006512 and A175080. Subsequence of A175072. Primes q with some results of {2, 28, 36, 52, 58, 66, ... } under first step of iteration of {r mod (max prime p < r)} starting at r = q, i.e. number 2 and primes q such that difference q and previous prime is equal to some of the values 2, 28, 36, 52, 58, 66, ...
Not the same as A094743: contains 2999, 3299, 5147, 5981, 8999, 9587, 10037, 10427, 10559, 10937, 11579, 12889, ... that are absent from that sequence. Up to 10^9, there are 3247366 terms in this sequence that are not in A094743, though every term from that sequence appears here. Is A094743 a subsequence of this sequence? - Charles R Greathouse IV, Jan 12 2022
It suffices to stop after the iterations yield a number less than 5 and check if the result is 2. Under this procedure, 2 takes 0 iterations, 5 is the first prime to take 1 iteration, 29 is the first to take 2 iterations, 2999 is the first to take 3 iterations, and 401429925999155063 is the first to take 4 iterations. - Charles R Greathouse IV, Jan 14 2022

Examples

			Iteration procedure for a(5) = 19: 19 mod 17 = 2. Iteration procedure for a(83) = 2999: 2999 mod 2971 = 28, 28 mod 23 = 5, 5 mod 3 = 2.

Links

Programs

  • Mathematica
    fQ[p_] := Block[{r = p}, While[r > 2, r = Mod[r, NextPrime[r, -1]]]; r == 2]; Select[ Prime@ Range@ 253, fQ] (* Robert G. Wilson v, Aug 09 2010 *)
  • PARI
    is(n)=if(!isprime(n), return(0)); while(n>4, n-=precprime(n-1)); n==2 \\ Charles R Greathouse IV, Jan 12 2022
  • PARI
    has(n)=while(n>4, n-=precprime(n-1)); n==2
list(lim)=my(v=List([2]),p=3); forprime(q=5,lim, if(has(q-p), listput(v,q)); p=q); Vec(v) \\ Charles R Greathouse IV, Jan 12 2022

Formula

A175072 \ A175076. [A-number corrected by R. J. Mathar, Sep 25 2010] - Jaroslav Krizek, Jan 30 2010

Extensions

More terms from Robert G. Wilson v, Aug 09 2010
A175080 inserted in comment - R. J. Mathar, Sep 25 2010

A094744 Rearrangement of primes so that sum of the absolute value of the successive differences is also a prime.

Original entry on oeis.org

2, 5, 3, 11, 7, 13, 19, 17, 23, 29, 47, 37, 67, 31, 43, 41, 53, 71, 59, 89, 61, 73, 79, 103, 83, 101, 107, 97, 109, 139, 127, 157, 131, 137, 113, 149, 167, 151, 163, 181, 193, 173, 197, 179, 191, 227, 251, 211, 277, 229, 271, 223, 307, 239, 263, 199, 241, 283, 257
Offset: 1

Views

Author

Amarnath Murthy, May 24 2004

Keywords

Comments

The smallest previously unused prime consistent with the definition is used at each step. - Franklin T. Adams-Watters, Oct 09 2006

Examples

			5-2 = 3 is prime, (5-2)+ (5-3) = 5 is a prime,(5-2)+(5-3)+(11-3) = 13 is a prime.

Links

Crossrefs

Cf. A094743, A094745.

Programs

  • Maple
    N:= 10000: # to use primes up to N
A[1]:= 2:
P:= select(isprime, [seq(i,i=3..N,2)]):
s:= 0:
for n from 2   do
  for i from 1 to nops(P) do
    if isprime(s + abs(P[i]-A[n-1])) then
      s:= s+abs(P[i]-A[n-1]);
      A[n]:= P[i];
      P:= subsop(i=NULL,P);
      break
    fi
  od;
  if not assigned(A[n]) then break fi;
od:
seq(A[i],i=1..n-1); # Robert Israel, Sep 16 2016

Extensions

Corrected and extended by Franklin T. Adams-Watters, Oct 09 2006

A094745 Primes arising as the partial sums of the successive differences in A094744.

Original entry on oeis.org

3, 5, 13, 17, 23, 29, 31, 37, 43, 61, 71, 101, 137, 149, 151, 163, 181, 193, 223, 251, 263, 269, 293, 313, 331, 337, 347, 359, 389, 401, 431, 457, 463, 487, 523, 541, 557, 569, 587, 599, 619, 643, 661, 673, 709, 733, 773, 839, 887, 929, 977, 1061, 1129, 1153
Offset: 1

Views

Author

Amarnath Murthy, May 24 2004

Keywords

Crossrefs

Cf. A094743, A094744.

Extensions

Corrected and extended by Franklin T. Adams-Watters, Oct 09 2006

A098933 Primes of the form p+14, where p is a prime.

Original entry on oeis.org

17, 19, 31, 37, 43, 61, 67, 73, 97, 103, 127, 151, 163, 181, 193, 211, 241, 271, 277, 283, 307, 331, 367, 373, 397, 433, 457, 463, 523, 571, 577, 601, 607, 613, 631, 661, 673, 691, 733, 757, 787, 811, 823, 853, 877, 967, 991, 997, 1033, 1063, 1117, 1123, 1201
Offset: 1

Views

Author

Douglas Winston (douglas.winston(AT)srupc.com), Oct 20 2004

Keywords

Crossrefs

Cf. A000040 A006512 A067829 A094743 A046132 A067830 A046117 A067831 A092402 A092146 A092216.

Programs

  • PARI
    isok(n) = isprime(n) && isprime(n - 14) \\ Michel Marcus, Jul 17 2013
Showing 1-4 of 4 results.

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