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 1-6 of 6 results.

A104718 Concatenations of pairs of primes that differ by 8.

Original entry on oeis.org

311, 513, 1119, 2331, 2937, 5361, 5967, 7179, 8997, 101109, 131139, 149157, 173181, 191199, 233241, 263271, 269277, 359367, 389397, 401409, 431439, 449457, 479487, 491499, 563571, 569577, 593601, 599607, 653661, 683691, 701709, 719727, 743751
Offset: 1

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Author

Jonathan Vos Post, Mar 20 2005

Keywords

Comments

There are no primes in this sequence after a(1) = 311, as all values thereafter are divisible by 3. Semiprimes in this sequence include: a(3) = 1119 = 3 * 373 a(6) = 5361 = 3 * 1787, a(8) = 7179 = 3 * 2393, a(9) = 8997 = 3 * 2999, a(10) = 101109 = 3 * 33703, a(13) = 173181 = 3 * 57727, a(15) = 233241 = 3 * 77747, a(17) = 269277 = 3 * 89759, a(21) = 431439 = 3 * 143813, a(26) = 569577 = 3 * 189859, a(35) = 821829 = 3 * 273943.

Crossrefs

Cf. A000040, A001358, A023202, A103195, A103206, A104719.

Formula

a(n) = A023202(n) concatenated with A023202(n)+8.

A103523 Concatenations of pairs of primes that differ by 100.

Original entry on oeis.org

3103, 7107, 13113, 31131, 37137, 67167, 73173, 79179, 97197, 127227, 139239, 151251, 157257, 163263, 181281, 193293, 211311, 283383, 331431, 349449, 367467, 379479, 409509, 421521, 457557, 463563, 487587, 499599, 541641, 547647, 577677
Offset: 1

Views

Author

Jonathan Vos Post, Mar 21 2005

Keywords

Comments

Integers in this sequence can never be prime, as, starting from the second one, they are all multiples of 3.

Examples

			9191019 is in this sequence because 919 is prime, 919+100 = 1019 is prime and 9191019 is the concatenation of those two primes differing by 100.

Links

Crossrefs

Cf. A000040, A001358, A023201, A100750, A103195, A103206, A104718, A104719.

Programs

  • Maple
    f:= proc(n) if isprime(n) and isprime(n+100) then 10^(1+ilog10(n+100))*n+n+100 fi end proc:
map(f, [3,seq(i,i=7..1000,6)]); # Robert Israel, Dec 07 2015
  • Mathematica
    FromDigits[Join@@IntegerDigits/@{#,#+100}]&/@Select[Prime@Range@200,PrimeQ[#+100]&] (* Giorgos Kalogeropoulos, Jul 04 2021 *)
  • Python
    from sympy import isprime, primerange as prange
def auptop(lim):
  return [int(str(p)+str(p+100)) for p in prange(2, lim+1) if isprime(p+100)]
print(auptop(577)) # Michael S. Branicky, Jul 04 2021

Formula

List: concatenate(p, p+100) iff p and p+100 are primes.

A103534 Concatenations of pairs of primes that differ by 1000.

Original entry on oeis.org

131013, 191019, 311031, 611061, 971097, 1031103, 1091109, 1511151, 1631163, 1811181, 1931193, 2231223, 2291229, 2771277, 2831283, 3071307, 3671367, 3731373, 4091409, 4331433, 4391439, 4871487, 4991499, 5231523, 5711571
Offset: 1

Views

Author

Jonathan Vos Post, Mar 22 2005

Keywords

Comments

All terms are multiples of 3.

Examples

			1811181 is in this sequence because 181 is prime, 181+1000 = 1181 is prime and those two primes are concatenated.

Crossrefs

Cf. A100750, A103195, A103206, A104718, A104719, A103523.

Programs

  • Mathematica
    10001#+1000&/@Select[Prime[Range[150]],PrimeQ[#+1000]&] (* Harvey P. Dale, Sep 01 2017 *)

Formula

a(n) = Concatenate(P, P+1000) iff P prime and P+1000 prime.

A103576 Concatenations of pairs of primes that differ by 1000000.

Original entry on oeis.org

31000003, 371000037, 1511000151, 1931000193, 1991000199, 2111000211, 3131000313, 3671000367, 3971000397, 4091000409, 4571000457, 5411000541, 5471000547, 5771000577, 6191000619, 6911000691, 8291000829, 8591000859
Offset: 1

Views

Author

Jonathan Vos Post, Mar 23 2005

Keywords

Comments

After the first element, 31000003, which is prime, integers in this sequence can never be prime, as they are all multiples of 3. They can be semiprimes, as is the case for 3671000367 = 3 x 1223666789, 4571000457 = 3 x 1523666819, 5411000541 = 3 x 1803666847, 9071000907 = 3 x 3023666969.

Examples

			Prime(47) = 211 and 211 + 1000000 = Prime(78515) = 1000211. Concatenating these two primes gives 2111000211 = 3^4 * 17^2 * 31 * 2909.

Crossrefs

Cf. A000040, A001358, A023201, A100750, A103195, A103206, A104718, A104719, A103523, A103534.

Formula

a(n) = Concatenate(P, P+1000000) iff P prime and P+1000000 prime.

A103617 Concatenations of pairs of primes that differ by 10^9.

Original entry on oeis.org

71000000007, 971000000097, 1031000000103, 1811000000181, 2231000000223, 2411000000241, 2711000000271, 3491000000349, 4091000000409, 4331000000433, 4391000000439, 6071000000607, 6131000000613, 7871000000787, 8291000000829
Offset: 1

Views

Author

Jonathan Vos Post, Mar 25 2005

Keywords

Comments

Integers in this sequence can never be prime, as they are all multiples of 3. They can be semiprimes, as is the case for Prime(42) concatenated with Prime(50847544) = 1811000000181 = 3 x 603666666727.

Examples

			181 is prime, 181+10^9 = 1000000181 is prime, so their concatenation is an element of this sequence: 1811000000181. Coincidentally, prime(181)+10^9 = 1000001087 is also prime.

Links

Crossrefs

Cf. A000040, A001358, A023201, A100750, A103195, A103206, A104718, A104719, A103523, A103534, A103576.

Programs

  • Mathematica
    FromDigits[Join[IntegerDigits[#],IntegerDigits[#+10^9]]]&/@Select[Prime[ Range[ 200]],PrimeQ[ #+ 10^9]&] (* Harvey P. Dale, May 14 2022 *)

Formula

a(n) = Concatenate(P, P+1000000000) iff P prime and P+1000000000 prime.

A104873 Concatenations of pairs of primes that differ by 10^12.

Original entry on oeis.org

611000000000061, 1631000000000163, 1931000000000193, 2111000000000211, 2711000000000271, 3311000000000331, 5471000000000547, 6611000000000661, 7511000000000751, 7871000000000787, 9971000000000997, 10511000000001051
Offset: 1

Views

Author

Jonathan Vos Post, Mar 29 2005

Keywords

Comments

Integers in this sequence can never be prime, as they are all multiples of 3. They can be semiprimes, as is the case for Prime(177) concatenated with Prime(37607912056) = 10511000000001051 = 3 * 3503666666667017.

Examples

			61 is prime, specifically prime(18) and 61 + 10^12 is prime, specifically prime(7607912020), so their concatenation is in this sequence: 611000000000061. The concatenation is not itself prime, as it equals 3 * 7 * 23 * 1265010351967.

Links

Crossrefs

Cf. A000040, A001358, A023201, A100750, A103195, A103206, A104718, A104719, A103523, A103534, A103576, A103617.

Programs

  • Mathematica
    #*10^13+10^12+#&/@Select[Prime[Range[200]],PrimeQ[#+10^12]&] (* Harvey P. Dale, Jan 18 2021 *)

Formula

a(n) = Concatenate(P, P+10^12) iff P prime and P+10^12 prime.
Showing 1-6 of 6 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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