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.

A384636 Triprimes that are the concatenation of three consecutive primes in reverse order.

Original entry on oeis.org

1175, 231917, 434137, 534743, 595347, 10310197, 107103101, 137131127, 149139137, 163157151, 167163157, 179173167, 223211199, 239233229, 251241239, 269263257, 281277271, 293283281, 311307293, 349347337, 383379373, 401397389, 419409401, 421419409, 449443439, 457449443, 487479467, 491487479
Offset: 1

Views

Author

Will Gosnell and Robert Israel, Jun 05 2025

Keywords

Examples

			a(3) = 434137 is a term because it is the concatenation in reverse order of the three consecutive primes 37, 41 and 43, and 434137 = 11 * 61 * 647 is the product of three primes.

Links

Crossrefs

Cf. A014612, A383114, A384638.

Programs

  • Maple
    cat3:= proc(a,b,c)
  (a*10^(1+ilog10(b))+b)*10^(1+ilog10(c))+c
end proc:
select(t -> numtheory:-bigomega(t) = 3, [seq(cat3(ithprime(i+2),ithprime(i+1),ithprime(i)),i=1..100)]);
  • Mathematica
    p3[p_]:=FromDigits[Join[IntegerDigits[Prime[p+2]],IntegerDigits[Prime[p+1]],IntegerDigits[Prime[p]]]];Select[Array[p3,100],PrimeOmega[#]==3&] (* James C. McMahon, Jun 09 2025 *)

A384638 Primes p such that the concatenations of three consecutive primes starting with p, in both forward and backwards orders, are triprimes.

Original entry on oeis.org

43, 47, 97, 101, 151, 157, 167, 199, 281, 293, 487, 601, 607, 809, 839, 967, 1013, 1069, 1129, 1223, 1249, 1259, 1289, 1361, 1367, 1543, 1571, 1663, 1753, 1861, 1871, 1873, 1997, 2141, 2281, 2551, 2593, 2909, 3121, 3271, 3313, 3361, 3371, 3461, 3823, 3881, 3907, 4019, 4211, 4289, 4327, 4349, 4451, 4513
Offset: 1

Views

Author

Will Gosnell and Robert Israel, Jun 05 2025

Keywords

Comments

Primes p such that if q and r are the next two primes, both concatenations p||q||r and r||q||p have three prime factors, counted with multiplicity.

Examples

			a(2) = 47 is a term because 47, 53, 59 are consecutive primes and both 475359 = 3 * 193 * 821 and 595347 = 3 * 191 * 1039 have three prime factors, counted with multiplicity.

Links

Crossrefs

Cf. A014612, A383114, A384636.

Programs

  • Maple
    cat3:= proc(a,b,c)
(a*10^(1+ilog10(b))+b)*10^(1+ilog10(c))+c
end proc;
R:= NULL: count:= 0: a:= 2: b:= 3: c:= 5:
for i from 1 while count < 100 do
  a:= b; b:= c; c:= nextprime(c);
  if numtheory:-bigomega(cat3(a,b,c)) = 3 and numtheory:-bigomega(cat3(c,b,a)) = 3 then
     R:= R,a; count:= count+1;
  fi
od:
R;
  • Mathematica
    Select[Prime[Range[612]],PrimeOmega[FromDigits[Join[IntegerDigits[#],IntegerDigits[NextPrime[#]],IntegerDigits[NextPrime[#,2]]]]]==3&&PrimeOmega[FromDigits[Join[IntegerDigits[NextPrime[#,2]],IntegerDigits[NextPrime[#,1]],IntegerDigits[#]]]]==3&] (* James C. McMahon, Jun 20 2025 *)

A385968 Triprimes that are concatenations of three consecutive primes, and whose prime factors sum to a prime.

Original entry on oeis.org

199211223, 331337347, 367373379, 487491499, 653659661, 859863877, 102110311033, 106910871091, 111711231129, 112911511153, 130313071319, 143914471451, 165716631667, 178918011811, 214321532161, 226722692273, 246724732477, 274127492753, 274927532767, 284328512857, 330133073313, 362336313637
Offset: 1

Views

Author

Will Gosnell and Robert Israel, Jul 13 2025

Keywords

Examples

			a(3) = 367373379 is a term because it is the concatenation of consecutive primes 367, 373 and 379 and is the product of three primes 3 * 19 * 6445147 such that 3 + 19 + 6445147 = 6445169 is prime.

Links

Crossrefs

Intersection of A107707 and A383114.

Programs

  • Maple
    tcat:= proc(a,b,c);
  c + 10^(1+ilog10(c))*(b + 10^(1+ilog10(b))*a)
end proc:
R:= NULL: count:= 0:
q:= 2: r:= 3:
while count < 100 do
  p:= q; q:= r; r:= nextprime(r);
  x:= tcat(p,q,r);
  F:= ifactors(x)[2];
  if add(t[2],t=F) = 3 and isprime(add(t[1]*t[2],t=F)) then
     count:= count+1; R:= R,x;
  fi;
od:
R;
  • Mathematica
    tp[p_]:=FromDigits[Join[IntegerDigits/@{Prime[p],Prime[p+1],Prime[p+2]}//Flatten]];Select[Array[tp,530],PrimeOmega[#]==3&&PrimeQ[Total[First/@FactorInteger[#]]]&] (* James C. McMahon, Jul 20 2025 *)

A384235 a(n) is the least number that is the concatenation of n consecutive primes, in increasing order, and is the product of n primes, counted with multiplicity.

Original entry on oeis.org

2, 35, 357, 11131719, 3571113, 5711131719, 463467479487491499503, 811821823827829839853857, 103910491051106110631069108710911093, 1291129713011303130713191321132713611367, 19011907191319311933194919511973197919871993, 109091093710939109491095710973109791098710993110031102711047
Offset: 1

Views

Author

Robert Israel, May 23 2025

Keywords

Examples

			a(4) = 11131719 is the concatenation of four consecutive primes 11, 13, 17, 19, and 11131719 = 3 * 17 * 167 * 1307 is the product of four primes.

Crossrefs

Cf. A383114.

Programs

  • Maple
    lcat:= proc(L) local r,i;
   r:= L[1];
   for i from 2 to nops(L) do
     r:= r * 10^(1+ilog10(L[i]))+L[i]
   od;
   r
end proc:
f:= proc(n) local i,j,x;
     for i from 1 do
       x:= lcat([seq(ithprime(j),j=i..i+n-1)]);
       if numtheory:-bigomega(x) = n then return x fi
     od;
end proc:
map(f, [$1..13]);
  • Mathematica
    a[n_]:=Module[{i=1},While[PrimeOmega[m={};Do[m=Join[m,IntegerDigits[Prime[j]]],{j,i,i+n-1}];ln=FromDigits[m]]!=n,i++];ln];Array[a,11] (* James C. McMahon, Jun 02 2025 *)
Showing 1-4 of 4 results.

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

Content is available under The OEIS End-User License Agreement.