A172035 -id:A172035 - cp's OEIS frontend

A172216 Smallest k such that sum of digits of prime(n)^k is prime.

1, 1, 1, 1, 1, 3, 2, 5, 1, 1, 7, 2, 1, 1, 1, 2, 5, 1, 1, 6, 2, 2, 1, 1, 4, 1, 4, 2, 2, 1, 2, 1, 1, 1, 2, 1, 1, 4, 6, 1, 1, 2, 1, 1, 1, 1, 3, 1, 1, 1, 5, 6, 1, 4, 4, 1, 1, 2, 2, 1, 1, 4, 3, 1, 1, 1, 1, 1, 8, 2, 1, 1, 2, 1, 1, 5, 2, 1, 1, 1, 8, 1, 4, 2, 3, 1, 1, 2, 1, 1, 1, 4, 1, 8, 3, 2, 6, 2, 3, 6, 2, 1, 10, 8, 1

Offset: 1

Klaus Brockhaus, Jan 29 2010

For all n, prime(n)^0 = 1 has nonprime sum of digits 1.

a(n) = 1 iff prime(n) is in A046704, an additive prime. a(n) = 1 iff n is in A075177.

			prime(1) = 2; 2^1 = 2 has prime sum of digits 2. Hence a(1) = 1.
prime(6) = 13; 13^1 = 13 has nonprime sum of digits 4; 13^2 = 169 has nonprime sum of digits 16; 13^3 = 2197 has prime sum of digits 19. Hence a(6) = 3.

Cf. A046704, A075177, A172035.

S:=[]; for n in [1..105] do j:=1; while not IsPrime(&+Intseq(NthPrime(n)^j)) do j+:=1; end while; Append(~S, j); end for; S;

sdp[n_]:=Module[{k=1},While[!PrimeQ[Total[IntegerDigits[Prime[n]^k]]], k++]; k]; Array[sdp,110] (* Harvey P. Dale, Apr 13 2014 *)

A178237 Smallest prime p of the form prime(n)+k^2 such that sum of digits(p) = prime(n).

Original entry on oeis.org

2, 3, 5, 7, 47, 157, 593, 919, 599, 66593, 46687, 396937, 467897, 467899, 6969647, 16499897, 367488959, 598095997, 2977884967, 4977866987, 2797986889, 58888728979, 58987779959, 679585896989, 4989996468997

Offset: 1

Ulrich Krug (leuchtfeuer37(AT)gmx.de), May 23 2010

It is still an open problem if there exist infinitely many primes of form k^2 + d (d integer, no negative square).

For n<=4, k=0 suffices: e.g. prime(1)+0^2=2 = sum of digits(prime(1)), so a(n)=prime(n).

			a(13) = 467897 because its digitsum is 41 which is the 13th prime, it is of the form prime(13)+k^2 with k=684, and it is the least such prime.

Cf. A000040, A172035, A176111, A176790

sod(n) = {digs = digits(n, 10); return (sum(j=1, #digs, digs[j]));}
a(n) = {k = 0; p = prime(n); while (! (isprime(q=p+k^2) && (sod(q) == p)), k++); return (q);} \\ Michel Marcus, Jul 26 2013

a(5) corrected and sequence extended by D. S. McNeil, May 25 2010

cp's OEIS Frontend

A172216 Smallest k such that sum of digits of prime(n)^k is prime.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Magma

Mathematica