A060288 -id:A060288 - cp's OEIS frontend

A060290 Primes which are sums of twin Harshad numbers (includes overlaps).

3, 5, 7, 11, 13, 17, 19, 41, 223, 401, 419, 449, 881, 1021, 1259, 1289, 1471, 1601, 1607, 1871, 1999, 2029, 2281, 2549, 2609, 2833, 3041, 3359, 3457, 4001, 4049, 4481, 4801, 4931, 5641, 6329, 7499, 7561, 8081, 8849, 8929, 9613, 9619, 10111, 10321

Offset: 1

Enoch Haga, Mar 24 2001

			a(5)=17, a prime because the first Harshad number is 8 and the second is 9 and 8+9=17. In this sequence overlapping Harshad's are permitted: 1+2=3 and 2+3=5.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A005349, A060159, A060288, A060289, A060291.

isA005349 := proc(n)
    if n mod digsum(n) = 0 then
        true;
    else
        false;
    end if;
end proc:
isA060290 := proc(n)
    local h1 ;
    if isprime(n) then
        h1 := (n-1)/2 ;
        if isA005349(h1) and isA005349(h1+1) then
            true;
        else
            false;
        end if;
    else
        false;
    end if;
end proc:
for n from 3 to 20000 do
    if isA060290(n) then
        printf("%d,",n) ;
    end if;
end do: # R. J. Mathar, Dec 20 2013

harshadQ[n_] := Divisible[n, Plus @@ IntegerDigits[n]]; s = {}; q1 = True; Do[q2 = harshadQ[n]; If[q1 && q2 && PrimeQ[2*n - 1], AppendTo[s, 2*n - 1]]; q1 = q2, {n, 2, 5000}]; s (* Amiram Eldar, Jan 19 2021 *)

20 A=0;
30 inc A;
40 if Ct=2 then Z=(A-1)+(A-2): if Z=prmdiv(Z) then print A-2; "+"; A-1; "="; Z; "/"; :inc Pt;
50 if Ct=2 then Ct=1:A=A-2;
60 X=1;
70 B=str(A);
80 L=len(B);
90 inc X;
100 S=mid(B,X,1);
110 V=val(S):W=W+V;
120 if XDt+1 then Ct=0:Dt=0;
150 Dt=Ct:W=0;
160 if A<=10 then 30;
170 print Pt;

{n in A000040: (n-1)/2 in A005349 and (n+1)/2 in A005349}. - R. J. Mathar, Dec 20 2013

Offset corrected by Amiram Eldar, Jan 19 2021

A060289 Number of distinct (non-overlapping) twin Harshad numbers whose sum is prime and where the 2nd Harshad is <= 10^n.

Original entry on oeis.org

4, 5, 17, 53, 250, 1404, 9013, 58608, 401614, 2908740, 21832530

Offset: 1

Enoch Haga, Mar 23 2001

			a(1)=4 because there are four pairs of Harshads whose sum is prime and the 2nd Harshad in the pair is <=10; these are 1+2=3, 3+4=7, 5+6=11, 9+10=19. 8+9=17 is not included because this pair overlaps 7+8=15, which also happens to be not prime. (Another sequence might include such overlapping pairs.)

Cf. A005349, A060159, A060288, A060290, A060291.

harshadQ[n_] := Divisible[n, Plus @@ IntegerDigits[n]]; c = 0; p = 10; s = {}; n = 0; k = 2; q1 = True; While[n <6, q2 = harshadQ[k]; If[q1 && q2, If[PrimeQ[2*k - 1],c++;If[k > p, n++; AppendTo[s, c-1]; p *= 10]]; q1 = False, q1 = q2];  k++]; s (* Amiram Eldar, Jan 19 2021 *)

Niven(n)=n%sumdigits(n)==0
a(n)=my(t,s); for(k=1,10^n,if(Niven(k), if(isprime(t+k), t=-10^n; s++); t=k)); s \\ Charles R Greathouse IV, Jan 23 2014

Generate the twin Harshads whose sum is prime. Count how many there are where the 2nd Harshad in the pair is <= a consecutive power of 10.

a(8)-a(11) from Amiram Eldar, Jan 19 2021

A060291 Number of twin Harshads, including overlaps, whose sum is prime and where the 2nd Harshad is <= 10^n.

Original entry on oeis.org

7, 8, 21, 60, 278, 1520, 9583, 61835, 419705, 3023007, 22597508

Offset: 1

Enoch Haga, Mar 24 2001

			a(1)=7 because there are 7 pairs of Harshads whose sum is prime and the 2nd Harshad in the pair is <= 10; these are 1+2=3, 2+3=5, 3+4=7, 5+6=11, 6+7=13, 8+9=17, 9+10=19. (Another sequence does not permit overlapping Harshad numbers.)

Cf. A060288, A060289, A060290, A005349, A060159.

harshadQ[n_] := Divisible[n, Plus @@ IntegerDigits[n]]; c = 0; p = 10; s = {}; n = 0; k = 2; q1 = True; While[n < 6, q2 = harshadQ[k]; If[q1 && q2 && PrimeQ[2*k-1], c++; If[k > p, n++; AppendTo[s, c-1]; p *= 10]]; q1 = q2; k++]; s (* Amiram Eldar, Jan 19 2021 *)

Generate the twin Harshads whose sum is prime. Count how many there are where the 2nd Harshad in the pair is <= to a consecutive power of 10.

a(8)-a(11) from Amiram Eldar, Jan 19 2021

cp's OEIS Frontend

A060290 Primes which are sums of twin Harshad numbers (includes overlaps).

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Maple

Mathematica

UBASIC

Formula

Extensions

A060289 Number of distinct (non-overlapping) twin Harshad numbers whose sum is prime and where the 2nd Harshad is <= 10^n.

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica

PARI

Formula

Extensions

A060291 Number of twin Harshads, including overlaps, whose sum is prime and where the 2nd Harshad is <= 10^n.

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica

Formula

Extensions