A089228 -id:A089228 - cp's OEIS frontend

A071149 Numbers n such that the sum of the first n odd primes (A071148) is prime; analogous to A013916.

1, 9, 15, 17, 53, 55, 61, 65, 71, 75, 95, 115, 117, 137, 141, 143, 155, 183, 191, 203, 249, 273, 275, 283, 291, 305, 339, 341, 377, 409, 411, 415, 435, 439, 449, 483, 495, 497, 509, 525, 583, 599, 605, 621, 633, 637, 643, 645, 671, 675, 709, 713, 715, 727

Offset: 1

Labos Elemer, May 13 2002

nonn

T. D. Noe, Table of n, a(n) for n = 1..1000

Cf. A007504, A013916, A013917, A013918, A065091, A071148, A071150, A089228.

Primes:= select(isprime, [seq(2*i+1,i=1..10^4)]):
L:= ListTools:-PartialSums(Primes):
select(i -> isprime(L[i]), [$1..nops(L)]); # Robert Israel, May 19 2015

Position[Accumulate@ Prime@ Range[2, 750], ?(PrimeQ@# &)] // Flatten (* _Robert G. Wilson v, May 19 2015, after Harvey P. Dale in A013916 *)

s=n=0; forprime(p=3,1e4, n++; if(isprime(s+=p), print1(n", "))) \\ Charles R Greathouse IV, May 13 2015

a(n) = pi(A071150(n)). - Charles R Greathouse IV, May 13 2015

A053845 Primes of form prime(1) + ... + prime(k) + 1.

Original entry on oeis.org

3, 11, 29, 59, 101, 239, 569, 1061, 1481, 1721, 4889, 5351, 6871, 22549, 23593, 25801, 29297, 35569, 38239, 41023, 71209, 77137, 87517, 94057, 105541, 120349, 122921, 125509, 128113, 133387, 138869, 141677, 156109, 159073, 165041, 183707

Offset: 1

Enoch Haga, Mar 28 2000

			prime(1) + 1 = 2 + 1 = 3 (prime, thus a(1));
prime(1) + prime(2) + 1 = 2 + 3 + 1 = 6 (nonprime);
prime(1) + prime(2) + prime(3) + 1 = 2 + 3 + 5 + 1 = 11 (prime, thus a(2)); etc. - _Jon E. Schoenfield_, Jan 09 2015

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A007504, A013918, A089228.

p=1;lst={};Do[p+=Prime[n];If[PrimeQ[p],AppendTo[lst,p]],{n,7!}];lst (* Vladimir Joseph Stephan Orlovsky, Jun 14 2009 *)

lista(nn) = {s = 1; for (n=1, nn, s += prime(n); if (isprime(s), print1(s, ", ")););} \\ Michel Marcus, Jan 10 2015

10 x=x+1; 20 if x<>prmdiv(x) then 10; 30 y=x; 40 r=r+y; 50 if r=prmdiv(r) then print r;:p=p+1; 60 if p<100 then 10

a(n) = A007504(A089228(n)) + 1. - Amiram Eldar, Apr 29 2024

A376891 Numbers k such that the sum of the first k lesser of twin primes is a lesser of twin prime.

Original entry on oeis.org

1, 23, 143, 251, 281, 305, 341, 455, 605, 761, 1349, 1613, 2765, 2903, 2981, 3623, 3725, 3923, 4049, 4133, 4745, 5207, 5303, 5489, 5765, 6515, 6611, 7793, 7835, 8153, 8237, 10427, 10697, 11261, 11447, 11627, 11729, 12401, 12701, 13871, 14327, 15359, 15683

Offset: 1

Ilya Gutkovskiy, Oct 08 2024

nonn

Robert Israel, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Twin Primes.

Cf. A001359, A013916, A071149, A086167, A089228, A376892.

K:= 1: count:= 1: s:= 3: k:= 1:
for p from 5 by 6 do
  if isprime(p) and isprime(p+2) then
    k:= k+1;
    s:= s+p;
    if s mod 6 = 5 and isprime(s) and isprime(s+2) then
      count:= count+1; K:= K,k;
      if count = 100 then break fi;
fi fi od:
K; # Robert Israel, Oct 08 2024

Position[Accumulate[Select[Partition[Prime[Range[200000]],2,1],#[[2]]-#[[1]]==2&][[;;,1]]],?(AllTrue[#+{0,2},PrimeQ]&)]//Quiet//Flatten (* _Harvey P. Dale, Jun 24 2025 *)

lista(nn) = my(v=select(p->isprime(p+2), primes(nn)), s = vector(#v)); s[1] = v[1]; for (i=2, #v, s[i] = s[i-1]+v[i]); Vec(select(x->(isprime(x) && isprime(x+2)), s, 1)); \\ Michel Marcus, Oct 10 2024

A376892 Numbers k such that the sum of the first k greater of twin primes is a greater of twin prime.

Original entry on oeis.org

1, 45, 105, 675, 987, 1431, 1593, 1677, 1785, 1875, 2037, 2541, 3039, 3045, 3051, 3183, 3267, 3531, 3699, 4113, 4239, 4377, 4443, 5643, 5673, 5709, 6027, 6543, 6615, 6771, 6891, 6915, 6999, 8043, 8109, 8313, 8607, 8739, 10197, 10569, 11103, 11139, 11361, 11787, 12045

Offset: 1

Ilya Gutkovskiy, Oct 08 2024

nonn

Robert Israel, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Twin Primes.

Cf. A006512, A013916, A071149, A086168, A089228, A376891.

K:= 1: count:= 1: s:= 5: k:= 1:
for p from 7 by 6 do
  if isprime(p) and isprime(p-2) then
    k:= k+1;
    s:= s+p;
    if s mod 6 = 1 and isprime(s) and isprime(s-2) then
      count:= count+1; K:= K, k;
      if count = 100 then break fi;
fi fi od:
K; # Robert Israel, Nov 08 2024

lista(nn) = my(v=select(p->isprime(p-2), primes(nn)), s = vector(#v)); s[1] = v[1]; for (i=2, #v, s[i] = s[i-1]+v[i]); Vec(select(x->(isprime(x) && isprime(x-2)), s, 1)); \\ Michel Marcus, Oct 10 2024

A264858 Integers k such that A007504(k) + 1 is a square.

Original entry on oeis.org

0, 17, 539, 652, 6420, 350857847

Offset: 1

Altug Alkan, Nov 26 2015

Integers k such that the sum of the first k primes + 1 is a square.
Integers k such that A014284(k+1) is a square.
In A110996, it is commented that a(6) > 250000, if it exists.
a(6) > 50000000, if it exists. - Jon E. Schoenfield, Nov 29 2015

			a(2) = 17 because A007504(17) + 1 = 440 + 1 = 441 is a square.

Cf. A007504, A014284, A033997, A089228, A110996.

t = Accumulate[Prime@ Range@ 100000]; Prepend[Select[Range@ 7000, IntegerQ@ Sqrt[t[[#]] + 1] &], 0] (* Michael De Vlieger, Nov 29 2015, after Zak Seidov at A007504 *)
Join[{0},Position[Accumulate[Prime[Range[6500]]]+1,?(IntegerQ[Sqrt[ #]]&)]] // Flatten (* _Harvey P. Dale, Feb 12 2018 *)

lista(nn) = { print1(0, ", "); s = 1; for(k=1, nn, s += prime(k); if(issquare(s), print1(k, ", ")););}

a(6) from Jinyuan Wang, Aug 09 2023

A277123 Numbers k such that 1 + Sum_{j=1..k} prime(j)^2 is prime.

Original entry on oeis.org

1, 11, 19, 29, 37, 73, 97, 155, 163, 175, 191, 257, 295, 313, 325, 341, 365, 389, 391, 409, 415, 461, 491, 497, 515, 599, 697, 715, 757, 761, 767, 775, 785, 793, 857, 875, 895, 899, 905, 919, 1099, 1109, 1117, 1139, 1151, 1163, 1225, 1271, 1279, 1295, 1309

Offset: 1

Alex Ratushnyak, Sep 30 2016

nonn

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A000040, A013916, A089228, A131694, A159260.

Position[Accumulate[Prime[Range[2000]]^2]+1,?PrimeQ]//Flatten (* _Harvey P. Dale, Sep 07 2019 *)

lista(nn) = for(n=1, nn, if(isprime(1+sum(i=1, n, prime(i)^2)), print1(n, ", "))); \\ Altug Alkan, Oct 01 2016

import sympy
sum = p = 1
for n in range(1,3001):
  while not sympy.isprime(p):  p+=1    # find the n'th prime
  sum += p*p
  p+=1
  if sympy.isprime(sum):  print(n, end=', ')

cp's OEIS Frontend

A071149 Numbers n such that the sum of the first n odd primes (A071148) is prime; analogous to A013916.

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Formula

A053845 Primes of form prime(1) + ... + prime(k) + 1.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

PARI

UBASIC

Formula

A376891 Numbers k such that the sum of the first k lesser of twin primes is a lesser of twin prime.

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

Mathematica

PARI

A376892 Numbers k such that the sum of the first k greater of twin primes is a greater of twin prime.

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

PARI

A264858 Integers k such that A007504(k) + 1 is a square.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

PARI

Extensions

A277123 Numbers k such that 1 + Sum_{j=1..k} prime(j)^2 is prime.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Python