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 1-7 of 7 results.

A134532 Numbers k such that the sum of the digits of 5^k is prime.

Original entry on oeis.org

1, 2, 4, 5, 6, 7, 13, 19, 20, 22, 26, 27, 29, 33, 34, 36, 41, 43, 44, 50, 54, 55, 58, 59, 60, 66, 69, 70, 74, 75, 81, 85, 91, 95, 97, 99, 100, 101, 110, 112, 125, 127, 129, 131, 133, 134, 136, 142, 143, 145, 146, 148, 153, 156, 157, 163, 165, 178, 187, 189, 190, 196
Offset: 1

Views

Author

Paolo P. Lava and Giorgio Balzarotti, Oct 30 2007

Keywords

Examples

			5^2=25 and 2+5=7 is prime.

Links

Crossrefs

Cf. A076203, A134533, A134534, A134535.

Programs

  • Maple
    P:=proc(k) if isprime(convert(convert(5^k,base,10),`+`)) then k; fi; end: seq(P(n),n=1..200);
  • Mathematica
    a={};For[n=1, n<200, n++, If[PrimeQ[Plus@@IntegerDigits[5^n]], AppendTo[a, n]]];a (* Vincenzo Librandi, Apr 17 2013 *)

Extensions

Corrected name and new Maple code by_Paolo P. Lava_, Jun 24 2024

A134533 Numbers n such that the sum of the digits of 7^n is prime.

Original entry on oeis.org

1, 2, 4, 8, 10, 12, 18, 19, 22, 24, 25, 32, 33, 35, 45, 56, 57, 58, 59, 60, 72, 73, 76, 81, 82, 84, 88, 100, 102, 103, 104, 105, 117, 118, 125, 136, 138, 142, 147, 149, 162, 188, 190, 192, 195, 201, 203, 206, 210, 212, 232, 240, 246, 252, 262, 264, 265, 269, 270, 280
Offset: 1

Views

Author

Paolo P. Lava and Giorgio Balzarotti, Oct 30 2007

Keywords

Examples

			7^2=49 and 4+9=13 is prime.

Links

Crossrefs

Cf. A076203, A134532, A134534, A134535.

Programs

  • Maple
    P:=proc(n) local cont,i,k,w; if isprime(n) then cont:=0; while cont<1000 do cont:=cont+1; w:=0; k:=n^cont; while k>0 do w:=w+k-(trunc(k/10)*10); k:=trunc(k/10); od; if isprime(w) then print(cont); fi; od; fi; end: P(7);
  • Mathematica
    a={}; For[n=1, n<700, n++, If[PrimeQ[Plus@@IntegerDigits[7^n]], AppendTo[a, n]]];a (* Vincenzo Librandi, Apr 17 2013 *)

A134534 Numbers n such that the sum of the digits of 11^n is prime.

Original entry on oeis.org

1, 9, 10, 11, 13, 15, 19, 21, 22, 25, 31, 32, 51, 52, 57, 58, 59, 62, 63, 68, 69, 70, 75, 76, 80, 81, 84, 91, 93, 95, 98, 99, 100, 101, 103, 107, 109, 114, 117, 124, 131, 132, 133, 135, 137, 139, 142, 153, 158, 159, 161, 164, 175, 176, 182, 190, 192, 194, 198, 207
Offset: 1

Views

Author

Paolo P. Lava and Giorgio Balzarotti, Oct 30 2007

Keywords

Examples

			11^9=2357947691 and 2+3+5+7+9+4+7+6+9+1=53 is prime.

Links

Crossrefs

Cf. A076203, A134532, A134533, A134535.

Programs

  • Maple
    P:=proc(n)local cont,i,k,w; if isprime(n) then cont:=0; while cont<1000 do cont:=cont+1; w:=0; k:=n^cont; while k>0 do w:=w+k-(trunc(k/10)*10); k:=trunc(k/10); od; if isprime(w) then print(cont); fi; od; fi; end: P(11);
  • Mathematica
    Select[Range[250],PrimeQ[Total[IntegerDigits[11^#]]]&] (* Harvey P. Dale, Sep 29 2012 *)

A134535 Numbers n such that the sum of the digits of 13^n is prime.

Original entry on oeis.org

3, 6, 10, 14, 15, 24, 30, 33, 34, 39, 40, 47, 53, 57, 61, 71, 75, 76, 80, 81, 83, 88, 89, 92, 102, 103, 106, 117, 131, 143, 144, 147, 154, 163, 170, 187, 198, 200, 205, 210, 212, 221, 227, 238, 240, 253, 255, 260, 262, 265, 271, 275
Offset: 1

Views

Author

Paolo P. Lava and Giorgio Balzarotti, Oct 30 2007

Keywords

Examples

			13^3=2197 and 2+1+9+7=19 is prime.

Links

Crossrefs

Cf. A076203, A134532, A134533, A134534.

Programs

  • Maple
    P:=proc(n) local cont,i,k,w; if isprime(n) then cont:=0; while cont<1000 do cont:=cont+1; w:=0; k:=n^cont; while k>0 do w:=w+k-(trunc(k/10)*10); k:=trunc(k/10); od; if isprime(w) then print(cont); fi; od; fi; end: P(13);
  • Mathematica
    Select[Range[250], PrimeQ[Total[IntegerDigits[13^#]]]&] (* Vincenzo Librandi, Apr 17 2013 *)

A118731 Numbers k such that 2^k has odd digit sum.

Original entry on oeis.org

0, 4, 5, 7, 8, 10, 12, 16, 18, 19, 20, 22, 23, 24, 25, 27, 28, 29, 30, 31, 34, 35, 38, 39, 40, 48, 49, 52, 53, 56, 59, 62, 63, 66, 68, 69, 72, 75, 81, 87, 88, 89, 92, 93, 94, 96, 97, 99, 100, 101, 104, 105, 108, 109, 110, 111, 114, 118, 119, 121, 125, 127, 131, 132, 133
Offset: 1

Views

Author

Zak Seidov, May 22 2006

Keywords

Crossrefs

Cf. A118732, A118735, A076203.

Programs

  • Mathematica
    Select[Range[0, 133], Mod[ Plus @@ IntegerDigits[2^# ], 2] == 1 &] (* Ray Chandler, Jun 10 2006 *)

A135076 Primes appearing in A001370.

Original entry on oeis.org

2, 7, 5, 11, 13, 7, 19, 19, 29, 31, 41, 37, 29, 43, 41, 37, 47, 61, 59, 67, 71, 61, 73, 79, 89, 109, 103, 89, 109, 107, 107, 113, 139, 151, 127, 137, 107, 113, 167, 173, 167, 181, 191, 173, 193, 223, 233, 211, 199, 229, 251, 239, 281, 251, 277, 281, 239, 241, 239, 269
Offset: 1

Views

Author

Zak Seidov, Nov 18 2007

Keywords

Examples

			a(1)=2 because with s=A076203(1)=1, 2^s=2 and sod(2)=2; sod(x)=sum of digits of x;
a(2)=7 because with s=A076203(2)=4, 2^s=16 and sod(16)=7.
a(7)=9 because with s=A076203(7)=12, 2^s=4096 and sod(4096)=19.
a(8)=9 because with s=A076203(8)=18, 2^s=262144 and sod(262144)=19.

Links

Crossrefs

Cf. A001370, A076203.

Programs

  • PARI
    lista(nn) = {for (n=1, nn, sd = sumdigits(2^n); if (isprime(sd), print1(sd, ", ")););} \\ Michel Marcus, Oct 13 2013

Formula

a(n)=A007953(2^A076203(n)).

Extensions

Name corrected by Michel Marcus, Oct 13 2013

A132791 Numbers k such that the sum of the digits of 4^k is prime.

Original entry on oeis.org

2, 4, 5, 6, 9, 10, 12, 14, 15, 17, 19, 20, 24, 26, 33, 34, 36, 46, 47, 48, 66, 73, 74, 79, 81, 82, 92, 98, 101, 103, 104, 106, 107, 110, 113, 118, 119, 126, 131, 132, 133, 136, 137, 143, 144, 145, 147, 151, 156, 158, 161, 164, 171, 181, 185, 192, 195, 198, 200, 204
Offset: 1

Views

Author

Jonathan Vos Post, Nov 17 2007

Keywords

Comments

This is the 4th row of a table which begins as follows.
A(j,k) = numbers k such that the sum of the digits of j^k is prime.
j | A(j,k)
--+-------------------------------------------------------
1 | none
2 | A076203
3 | none (3 | sum of digits)
4 | 2, 4, 5, 6, 9, 10, 12, 14, 15, 17, ... (this sequence)
5 | 1, 2, 4, 5, 6, 7, 19, ...

Examples

			a(1) = 2 because digit sum(4^2) = digit sum(16) = 1+6 = 7.
a(2) = 4 because digit sum(4^4) = digit sum(256) = 13.
a(3) = 5 because digit sum(4^5) = digit sum(1024) = 7.
a(4) = 6 because digit sum(4^6) = digit sum(4096) = 19.
a(5) = 9 because digit sum(4^9) = digit sum(262144) = 19.
a(6) = 10 because digit sum(4^10) = digit sum(1048576) = 31.
a(7) = 12 because digit sum(4^12) = digit sum(16777216) = 37.
a(8) = 14 because digit sum(4^14) = digit sum(268435456) = 43.
a(9) = 15 because digit sum(4^15) = digit sum(1073741824) = 37.
a(10) = 17 because digit sum(4^17) = digit sum(17179869184) = 61.

Crossrefs

Cf. A000040, A000302, A007953, A076203.

Programs

  • Maple
    sd:=proc(n) options operator, arrow: add(convert(n, base, 10)[j], j=1..nops(convert(n, base, 10))) end proc: a:=proc(n) if isprime(sd(4^n)) = true then n else end if end proc: seq(a(n),n=1..150); # Emeric Deutsch, Nov 24 2007
  • Mathematica
    Select[Range[500], PrimeQ[Plus @@ IntegerDigits[4^# ]] &] (* Stefan Steinerberger, Nov 20 2007 *)

Formula

Numbers k such that A007953(A000302(k)) is in A000040.

Extensions

More terms from Stefan Steinerberger and Emeric Deutsch, Nov 20 2007
Edited by Jon E. Schoenfield, May 11 2019
Showing 1-7 of 7 results.

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