A134118 -id:A134118 - cp's OEIS frontend

A134117 Primes p such that q-p = 36, where q is the next prime after p.

9551, 12853, 14107, 15823, 18803, 22193, 22307, 22817, 24281, 27143, 28351, 29881, 32261, 40387, 42863, 45083, 45197, 46771, 46957, 47981, 50461, 57601, 60041, 60457, 62423, 65993, 66301, 68171, 69073, 69557, 71597, 72577, 72823, 73783

Offset: 1

Rick L. Shepherd, Oct 08 2007

nonn

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Index entries for primes, gaps between

Cf. A134116, A134118.

Select[Partition[Prime[Range[10000]],2,1],#[[2]]-#[[1]]==36&][[All,1]] (* Harvey P. Dale, Aug 27 2019 *)

is(n)=nextprime(n+1)==n+36 && isprime(n) \\ Charles R Greathouse IV, Sep 14 2015

a(n) >> n log^2 n. - Charles R Greathouse IV, Sep 14 2015

A271347 Primes p such that p + 38 is also prime.

Original entry on oeis.org

3, 5, 23, 29, 41, 59, 71, 89, 101, 113, 173, 191, 233, 239, 269, 293, 311, 359, 383, 401, 419, 449, 461, 503, 509, 563, 569, 593, 653, 701, 719, 773, 821, 839, 881, 929, 953, 971, 983, 1013, 1031, 1049, 1091, 1163, 1193, 1259, 1283, 1289

Offset: 1

Karl V. Keller, Jr., Apr 04 2016

nonn

A134118 is a subsequence of this sequence.

			3 such that 3 + 38 = 41 is also prime.
5 such that 5 + 38 = 43 is also prime.

Karl V. Keller, Jr., Table of n, a(n) for n = 1..10000

Cf. A000040, A134118.

Select[Prime[Range[250]], PrimeQ[# + 38] &] (* Alonso del Arte, Apr 05 2016 *)

lista(nn) = forprime(p=2, nn, if(ispseudoprime(p+38), print1(p, ", "))); \\ Altug Alkan, Apr 05 2016

from sympy import isprime
for i in range(3, 2001,2):
  if isprime(i) and isprime(i+38): print (i,end=', ')

A174350 Square array: row n >= 1 lists the primes p for which the next prime is p+2n; read by antidiagonals.

Original entry on oeis.org

3, 5, 7, 11, 13, 23, 17, 19, 31, 89, 29, 37, 47, 359, 139, 41, 43, 53, 389, 181, 199, 59, 67, 61, 401, 241, 211, 113, 71, 79, 73, 449, 283, 467, 293, 1831, 101, 97, 83, 479, 337, 509, 317, 1933, 523, 107, 103, 131, 491, 409, 619, 773, 2113, 1069, 887

Offset: 1

Clark Kimberling, Mar 16 2010

Every odd prime p = prime(i), i > 1, occurs in this array, in row (prime(i+1) - prime(i))/2. Polignac's conjecture states that each row contains an infinite number of indices. In case this does not hold, we can use the convention to continue finite rows with 0's, to ensure the sequence is well defined. - M. F. Hasler, Oct 19 2018

A permutation of the odd primes (A065091). - Robert G. Wilson v, Sep 13 2022

			Upper left hand corner of the array:
     3     5    11    17    29    41    59    71   101 ...
     7    13    19    37    43    67    79    97   103 ...
    23    31    47    53    61    73    83   131   151 ...
    89   359   389   401   449   479   491   683   701 ...
   139   181   241   283   337   409   421   547   577 ...
   199   211   467   509   619   661   797   997  1201 ...
   113   293   317   773   839   863   953  1409  1583 ...
  1831  1933  2113  2221  2251  2593  2803  3121  3373 ...
   523  1069  1259  1381  1759  1913  2161  2503  2861 ...
  (...)
Row 1: p(2) = 3, p(3) = 5, p(5) = 11, p(7) = 17,... these being the primes for which the next prime is 2 greater: (lesser of) twin primes A001359.
Row 2: p(4) = 7, p(6) = 13, p(8) = 19,... these being the primes for which the next prime is 4 greater: (lesser of) cousin primes A029710.

Robert G. Wilson v, Falling antidiagonals 1..115, flattened (first 50 from T. D. Noe).
Fred B. Holt and Helgi Rudd, On Polignac's Conjecture, arxiv:1402.1970 [math.NT], 2014.

Cf. A000040, A001223, A065091, A174349.
Rows 1, 2, 3, ...: A001359, A029710, A031924, A031926, A031928 (row 5), A031930, A031932, A031934, A031936, A031938 (row 10), A061779, A098974, A124594, A124595, A124596 (row 15), A126784, A134116, A134117, A134118, A126721 (row 20), A134120, A134121, A134122, A134123, A134124 (row 25), A204665, A204666, A204667, A204668, A126771 (row 30), A204669, A204670.
Rows 35, 40, 45, 50, ...: A204792, A126722, A204764, A050434 (row 50), A204801, A204672, A204802, A204803, A126724 (row 75), A184984, A204805, A204673, A204806, A204807 (row 100); A224472 (row 150).
Column 1: A000230.
Column 2: A046789.

rows = 10; t2 = {}; Do[t = {}; p = Prime[2]; While[Length[t] < rows - off + 1, nextP = NextPrime[p]; If[nextP - p == 2*off, AppendTo[t, p]]; p = nextP]; AppendTo[t2, t], {off, rows}]; Table[t2[[b, a - b + 1]], {a, rows}, {b, a}] (* T. D. Noe, Feb 11 2014 *)
t[r_, 0] = 2; t[r_, c_] := Block[{p = NextPrime@ t[r, c - 1], q}, q = NextPrime@ p; While[ p + 2r != q, p = q; q = NextPrime@ q]; p]; Table[ t[r - c + 1, c], {r, 10}, {c, r, 1, -1}] (* Robert G. Wilson v, Nov 06 2020 *)

A174350_row(g, N=50, i=0, p=prime(i+1), L=[])={g*=2; forprime(q=1+p, , i++; if(p+g==p=q, L=concat(L, q-g); N--||return(L)))} \\ Returns the first N terms of row g. - M. F. Hasler, Oct 19 2018

a(n) = A000040(A174349(n)). - Michel Marcus, Mar 30 2016

Definition corrected and other edits by M. F. Hasler, Oct 19 2018

A320717 Indices of primes followed by a gap (distance to next larger prime) of 38.

Original entry on oeis.org

3302, 4052, 4154, 4743, 5093, 5229, 5782, 5902, 6131, 6406, 6802, 7145, 7164, 7399, 7718, 7789, 8303, 8782, 9237, 9957, 10073, 10431, 10465, 10541, 10549, 10580, 10981, 11244, 11818, 11853, 12147, 12574, 13094, 13237, 13286, 13337, 13435, 13669, 13906, 14186, 14270, 14301, 14380, 14397

Offset: 1

M. F. Hasler, Oct 19 2018

nonn

Indices of the primes listed in A134118.

Index entries for primes, gaps between.

Cf. A029707, A029709 (analog for gaps 2 & 4), A320701, A320702, ... A320720 (analog for gaps 6, 8, ..., 44), A116493 (gap 70), A116496 (gap 100), A116497 (gap 200), A116495 (gap 210).
Equals A000720 o A134118.
Indices of 38's in A001223.
Row 19 of A174349.

A(N=100,g=38,p=2,i=primepi(p)-1,L=List())={forprime(q=1+p,,i++; if(p+g==p=q, listput(L,i); N--||break));Vec(L)} \\ returns the list of first N terms of the sequence

a(n) = A000720(A134118(n)).

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A134117 Primes p such that q-p = 36, where q is the next prime after p.

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A271347 Primes p such that p + 38 is also prime.

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A174350 Square array: row n >= 1 lists the primes p for which the next prime is p+2n; read by antidiagonals.

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A320717 Indices of primes followed by a gap (distance to next larger prime) of 38.

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Formula