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 1-3 of 3 results.

A089396 Smallest n-digit term of A089395.

Original entry on oeis.org

1, 12, 106, 1018, 10312, 105502, 1197058, 11056216
Offset: 0

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Author

Amarnath Murthy, Nov 10 2003

Keywords

Examples

			a(3) = 256 which is the smallest 3-digit number such that 2*56 + 1 = 113, 25*6 + 1 = 151 and 256 + 1 = 257 are all prime.
		

Crossrefs

Programs

  • Maple
    with(combinat): ds:=proc(s) local j: RETURN(add(s[j]*10^(j-1),j=1..nops(s))):end: for d from 1 to 7 do sch:=[seq([1,op(i),d+1],i=[[],seq([j],j=2..d)])]: for n from 10^(d-1) to 10^d-1 do sn:=convert(n,base,10): fl:=0: for s in sch do m:=mul(j,j=[seq(ds(sn[s[i]..s[i+1]-1]),i=1..nops(s)-1)])+1: if not isprime(m) then fl:=1: break fi od: if fl=0 then printf("%d, ",n):break fi od od: # C. Ronaldo

Extensions

Corrected and extended by C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 25 2004
One more term (a(7)) from Harvey P. Dale, Mar 23 2019

A089397 Largest n-digit member of A089395.

Original entry on oeis.org

6, 82, 982, 9748, 96052, 992548
Offset: 1

Views

Author

Amarnath Murthy, Nov 10 2003

Keywords

Crossrefs

Programs

  • Maple
    with(combinat): ds:=proc(s) local j: RETURN(add(s[j]*10^(j-1),j=1..nops(s))):end: for d from 1 to 6 do sch:=[seq([1,op(i),d+1],i=[[],seq([j],j=2..d)])]: for n from 10^d-1 by -1 to 10^(d-1) do sn:=convert(n,base,10): fl:=0: for s in sch do m:=mul(j,j=[seq(ds(sn[s[i]..s[i+1]-1]),i=1..nops(s)-1)])+1: if not isprime(m) then fl:=1: break fi od: if fl=0 then printf("%d, ",n):break fi od od: # C. Ronaldo

Extensions

More terms from C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 25 2004

A089696 Numbers k such that the numbers obtained by placing as many '*' signs as possible anywhere between the digits and then adding 1 yields a prime in every case: let abc.. be the digits of k, then abc+1, a*bc+1, ab*c+1, a*b*c+1, ... must all be primes.

Original entry on oeis.org

1, 2, 4, 6, 12, 16, 22, 28, 36, 52, 58, 66, 82, 112, 136, 166, 256, 352, 556, 562, 586, 616, 652, 658
Offset: 0

Views

Author

Amarnath Murthy, Nov 10 2003

Keywords

Comments

Though the first 14 terms match with that of A089395, the next term of A089395 306 is not a member of this sequence. Conjecture: Sequence is finite.
No more terms < 10^7. The first 13 terms match with that of A089395, but A089395(14) = 106 is not included because 1*0*6+1 = 1 is not prime. - David Wasserman, Oct 04 2005

Examples

			256 is a member 256+1, 2*56 +1, 25*6+1, 2*5*6 +1 are all prime.
		

Crossrefs

Cf. A089695.

Programs

  • Maple
    with(combinat): ds:=proc(s) local j: RETURN(add(s[j]*10^(j-1),j=1..nops(s))):end: for d from 1 to 6 do sch:=[seq([1,op(i),d+1],i=choose([seq(j,j=2..d)]))]: for n from 10^(d-1) to 10^d-1 do sn:=convert(n,base,10): fl:=0: for s in sch do m:=mul(j,j=[seq(ds(sn[s[i]..s[i+1]-1]),i=1..nops(s)-1)])+1: if not isprime(m) then fl:=1: break fi od: if fl=0 then printf("%d, ",n) fi od od: # C. Ronaldo

Extensions

Corrected and extended by C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 25 2004
Showing 1-3 of 3 results.