A050434 -id:A050434 - cp's OEIS frontend

A116496 Numbers k such that difference between k-th prime and next prime is 100.

33608, 66762, 100978, 124508, 125049, 172619, 202315, 233905, 256422, 286306, 306691, 320569, 326694, 334412, 362134, 374275, 382591, 395155, 414640, 428335, 440270, 467181, 493060, 511698, 518536, 555912, 561795, 567479, 590434, 592581

Offset: 1

Zak Seidov, Feb 18 2006

nonn

			p(33609) - p(33608) = 396833 - 396733 = 100.

Harvey P. Dale, Table of n, a(n) for n = 1..1000
Index entries for primes, gaps between

Cf. A050434, A116493, A116495, A116497.

PrimePi/@Transpose[Select[Partition[Prime[Range[600000]],2,1],#[[2]]-#[[1]] == 100&]][[1]] (* Harvey P. Dale, Sep 22 2013 *)

lista(nn) = {my(i=0, q=2); forprime(p=3, nn, i++; if(p-q==100, print1(i, ", ")); q=p); } \\ Jinyuan Wang, Jan 29 2020

A050434(n) = prime(a(n)). - R. J. Mathar, Apr 30 2024

A126784 Primes p such that q-p = 32, where q is the next prime after p.

Original entry on oeis.org

5591, 10799, 27701, 27851, 33647, 39047, 41081, 41687, 43721, 44417, 45989, 47459, 50789, 52457, 55259, 55547, 61781, 62351, 64817, 66239, 67307, 69959, 73907, 79907, 80567, 82307, 84089, 88037, 94169, 94961, 99191, 99929, 100559, 102611

Offset: 1

Douglas Winston (douglas.winston(AT)srupc.com), Feb 24 2007

Lower prime of a difference of 32 between consecutive primes.

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A001359, A029710, A031924, A031926, A031928, A031930, A031932, A031934, A031936, A031938, A061779, A098974, A124594, A124595, A124596, A000230, A050434.

lista(nn) = {p = 2; while (p < nn, q = nextprime(p+1); if (q - p == 32, print1(p, ", ")); p = q;);} \\ Michel Marcus, Jul 17 2013

A290450 Primes with property that the next prime has the same last digit.

Original entry on oeis.org

139, 181, 241, 283, 337, 409, 421, 547, 577, 631, 691, 709, 787, 811, 829, 887, 919, 1021, 1039, 1051, 1153, 1171, 1249, 1399, 1471, 1627, 1637, 1699, 1723, 1801, 1879, 2017, 2029, 2053, 2089, 2143, 2521, 2647, 2719, 2731, 2767, 2887, 2917, 3001, 3089, 3109, 3361, 3413, 3517, 3547, 3571

Offset: 1

Alonso del Arte, Aug 06 2017

Starts off the same as A031928, primes p such that the next prime is p + 10. First term that differs is 887, since 897 = 3 * 13 * 23 and the next prime is 907.
As the primes get larger and more sparsely distributed, the difference between successive primes is less likely to be less than 10.
One might expect that a prime is 1/4 as likely to be followed by a prime with the same least significant digit in base 10 (since the possibilities are 1, 3, 7, 9).
One might also expect this sequence to consist of a quarter of the primes. And yet pi(a(50)) = pi(3547) = 497; the 200th prime is 1223.

			139 is in the sequence because the immediately following prime is 149, which also ends in 9.
But 149 is not in the sequence because the next prime after that one is 151, which ends in 1, not 9.

Marius A. Burtea, Table of n, a(n) for n = 1..5005
Evelyn Lamb, "Peculiar Pattern Found in 'Random' Prime Numbers", Nature, March 14, 2016, republished by Scientific American.
Robert J. Lemke Oliver and Kannan Soundararajan, Unexpected biases in the distribution of consecutive primes, arXiv preprint arXiv:1603.03720 [math.NT], submitted on March 11, 2016.

Cf. A031928 (subset), A050434 (with 2 digits).

f:=func; a:=[]; for p in PrimesUpTo(4000) do if f(p,1) or f(p,3) or f(p,7) or f(p,9) then Append(~a,p); end if; end for; a; // Marius A. Burtea, Oct 16 2019

Select[Partition[Prime[Range[1000]], 2, 1], Mod[#[[1]], 10] == Mod[#[[2]], 10] &][[All, 1]] (* Harvey P. Dale, Aug 21 2017 *)
Module[{nn=1000,prs,p},prs=Prime[Range[nn]];p=Divisible[#,10]&/@ Differences[prs];Pick[Most[prs],p]] (* Harvey P. Dale, Aug 22 2017 *)

A031928 UNION A031938 UNION A124596 UNION A126721 UNION ... - R. J. Mathar, Jan 23 2022

A118590 Larger of two consecutive primes whose positive difference is a square.

Original entry on oeis.org

3, 11, 17, 23, 41, 47, 71, 83, 101, 107, 113, 131, 167, 197, 227, 233, 281, 311, 317, 353, 383, 401, 443, 461, 467, 491, 503, 617, 647, 677, 743, 761, 773, 827, 857, 863, 881, 887, 911, 941, 971, 1013, 1091, 1097, 1217, 1283, 1301, 1307, 1427, 1433, 1451, 1487

Offset: 1

Cino Hilliard, May 07 2006

			7 and 11 are consecutive primes. 11-7 = 4 a square, so 11 is the second term in the table.

T. D. Noe, Table of n, a(n) for n = 1..1000
Index entries for primes, gaps between

Cf. A031935, A031505, A134117 (gap 6^2), A204670 (gap 8^2), A050434 (gap 10^2), A138198, A161002.

Select[Table[Prime[n], {n, 2, 237}], IntegerQ[Sqrt[# - Prime[PrimePi[# - 1]]]] &] (* Jayanta Basu, Apr 23 2013 *)
nn = 500; ps = Prime[Range[nn]]; t = {}; Do[If[IntegerQ[Sqrt[ps[[n]] - ps[[n-1]]]], AppendTo[t, ps[[n]]]], {n, 2, nn}]; t (* T. D. Noe, Apr 23 2013 *)
Prime[#+1]&/@Flatten[Position[Differences[Prime[Range[250]]],?(IntegerQ[ Sqrt[#]]&)]] (* _Harvey P. Dale, May 08 2019 *)

g(n) = for(x=2, n, if(issquare(prime(x)-prime(x-1)), print1(prime(x)",")))

Superset of A031935 and A031505. [From R. J. Mathar, Aug 08 2008]

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

A194430 Integers m such that 6m+1 and 6m+101 are two consecutive primes.

Original entry on oeis.org

66122, 139708, 218911, 274680, 275951, 390998, 464062, 542493, 599248, 674526, 726567, 761851, 777592, 797312, 868518, 899766, 921381, 953983, 1004547, 1040377, 1071537, 1141977, 1209861, 1259061, 1277086, 1376176, 1391747, 1406978, 1467815

Offset: 1

Zak Seidov, Dec 21 2012

nonn

Zak Seidov, Table of n, a(n) for n = 1..3892

Cf. A050434.

{for(n=1,10^6,if(isprime(p=6*n+1)&&nextprime(p+2)==p+100,print1(n", ")))}

a(n) = (A050434(n)-1)/6.

A289908 Primes followed with prime gap configuration {100,2,100}.

Original entry on oeis.org

296468041, 1870871389, 1886253361, 2022370111, 2094362437, 2321196499, 2321944771, 3153215239, 3861098047, 4092880819, 4190128849, 4462557661, 4661412919, 4854695257, 5023173829, 5395034581, 5553579667, 5854691581, 6593477851, 6720677011, 7163334961, 7231579249

Offset: 1

Zak Seidov, Jul 15 2017

nonn

Primes prime(i) such that prime(i+1) = prime(i)+100, prime(i+2) = prime(i+1)+2, and prime(i+3) = prime(i+2)+100.

Subsequence of A050434.

A330678 First of two consecutive prime numbers both of which end with the digits 0,1.

Original entry on oeis.org

13200001, 14272201, 18494401, 20583601, 21699901, 27615001, 34697701, 37661101, 44561401, 52399801, 60096901, 61571701, 64683301, 67659301, 74313301, 76605301, 80451001, 85268401, 92287801, 92898301, 95076901, 96184801, 101931601, 112800001, 114759901

Offset: 1

Harvey P. Dale, Mar 01 2020

			20583601 is a prime and the next prime is 20583701, both which end in 0,1.

Cf. A050434.

Select[Partition[Prime[Range[10000000]],2,1],Mod[#[[1]],100]==Mod[+#[[2]], 100]==1&][[All,1]]

cp's OEIS Frontend

A116496 Numbers k such that difference between k-th prime and next prime is 100.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A126784 Primes p such that q-p = 32, where q is the next prime after p.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI

A290450 Primes with property that the next prime has the same last digit.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Magma

Mathematica

Formula

A118590 Larger of two consecutive primes whose positive difference is a square.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula

Extensions

A194430 Integers m such that 6m+1 and 6m+101 are two consecutive primes.

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

Formula

A289908 Primes followed with prime gap configuration {100,2,100}.

Views

Author

Keywords

Comments

Crossrefs

A330678 First of two consecutive prime numbers both of which end with the digits 0,1.

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica