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.

A146760 Last prime subtrahend at 10^n in A146759.

Original entry on oeis.org

5, 61, 997, 9929, 97283, 999983, 9999973, 99897341, 999999929, 9993948257, 99999999761, 999999999989, 9999516957181, 99999999999929, 999999999999989, 9999999999998857, 99999429057832259, 999999999999999989, 9999990391470218071
Offset: 1

Views

Author

Enoch Haga, Nov 02 2008

Keywords

Comments

It is not necessary to compute A146759 to compute this sequence. a(n) is the largest prime p<=10^n such that c(p)-p is also a prime, where c(p) is the smallest cube exceeding p. - Sean A. Irvine, Mar 27 2013

Examples

			A(2)=61 because 61 is the 7th and last prime subtrahend under 10^3.

Links

Crossrefs

Cf. A146756, A146757, A146759.

Programs

  • UBASIC
    10 'cu less pr are prime
20 N=1:O=1:C=1
30 A=3:S=sqrt(N):if N>10^3 then print N,C-1:stop
40 B=N\A
50 if B*A=N then 100
60 A=A+2
70 if A<=S then 40
80 R=O^3:Q=R-N
90 if N1 print R;N;Q;C:N=N+2:C=C+1:goto 30
100 N=N+2:if N

Extensions

More terms from Sean A. Irvine, Mar 27 2013

A146757 Number of primes p < 10^n such that s - p is prime, where s is the next square greater than p.

Original entry on oeis.org

2, 15, 68, 363, 2084, 13567, 95164, 705036, 5444255, 43211106, 351904307, 2921904565
Offset: 1

Views

Author

Enoch Haga, Nov 02 2008

Keywords

Comments

The number of primes p in the range 2 <= p <= 10^n for which The distance to the next larger square (A068527(p)) is also a prime. - R. J. Mathar, Sep 26 2011

Examples

			A(2) = 15 because at 10^2 there are 15 primes that, subtracted from the next higher value square, produce prime differences: {2, 7, 11, 13, 23, 29, 31, 47, 53, 59, 61, 79, 83, 89, 97}.

Crossrefs

Cf. A146315, A146758, A146759, A146760.

Programs

  • Mathematica
    Table[Length[Select[Prime[Range[PrimePi[10^n]]], PrimeQ[Ceiling[Sqrt[#]]^2 - #] &]], {n, 6}] (* T. D. Noe, Mar 31 2013 *)
  • UBASIC
    10 'sq less pr are prime 20 N=1:O=1:C=1 30 A=3:S=sqrt(N):if N>10^3 then print N,C-1:stop 40 B=N\A 50 if B*A=N then 100 60 A=A+2 70 if A<=S then 40 80 R=O^2:Q=R-N 90 if N1 print R;N;Q;C:N=N+2:C=C+1:goto 30 100 N=N+2:if N

Extensions

Name clarified by T. D. Noe, Mar 31 2013
a(8)-a(12) from Chai Wah Wu, Jun 22 2019

A146758 Last prime subtrahend at 10^n in A146757.

Original entry on oeis.org

7, 97, 983, 9941, 99839, 999983, 9998239, 99999989, 999950881, 9999999929, 99999999833, 999999999989, 9999999999863, 99999999999971, 999999961946087, 9999999999999917, 99999999989350667, 999999999999999989
Offset: 1

Views

Author

Enoch Haga, Nov 02 2008

Keywords

Examples

			A(2)=97 because 97 is the 15th and last prime difference under 10^2.

Crossrefs

Cf. A146757, A146759, A146760.

Programs

  • Maple
    A146758 := proc(n) local p: p:=10^n: do p:=prevprime(p): if(isprime(ceil(evalf(sqrt(p)))^2-p))then return p: fi: od: end: seq(A146758(n),n=1..14); # Nathaniel Johnston, Oct 01 2011
  • UBASIC
    10 'sq less pr are prime 20 N=1:O=1:C=1 30 A=3:S=sqrt(N):if N>10^3 then print N,C-1:stop 40 B=N\A 50 if B*A=N then 100 60 A=A+2 70 if A<=S then 40 80 R=O^2:Q=R-N 90 if N1 print R;N;Q;C:N=N+2:C=C+1:goto 30 100 N=N+2:if N

Extensions

a(8)-a(18) from Nathaniel Johnston, Oct 01 2011
Showing 1-3 of 3 results.

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

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