A084046 -id:A084046 - cp's OEIS frontend

A084047 Smallest prime p such that p - n is an n-th power, or 0 if no such number exists; i.e., smallest prime of the form k^n + n.

2, 3, 11, 5, 37, 7, 268435463, 6569, 521, 11, 36028797018963979, 13, 859935929762876868984659981, 4807339234680508004200143948920808143, 32783, 17, 30491346729331195921, 19, 32064977213018365645815827, 147808829414345923316083210206383297621

Offset: 1

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 26 2003

A072883 is the main entry for the problem of finding the smallest prime of the form k^n + n: many such k (up to n = 750 and beyond) are listed in the b-file there, but the corresponding primes are too large to list more of them here. - M. F. Hasler, Jul 07 2024

			a(2) = 3 = 1^2 + 2; a(4) = 5 = 1^4 + 4; a(6) = 7 = 1^6 + 6.

Barry Carter, Tweaks to A084047 (request), in r/OEIS on reddit.com, May 8, 2023.

Cf. A084046, A072883.

f[n_] := f[n] = Module[{m=1}, While[!PrimeQ[m^n + n], m++]; Return[m^n + n]]; (* from Barry Carter in r/OEIS, May 08 2023, cf. link. - M. F. Hasler, Jul 07 2024 *)

A084047(n, k=A072883(n))=if(k, k^n + n, 0) \\ M. F. Hasler, Jul 07 2024

In general, if n+1 is prime, then a(n) = n + 1 = 1^n + n.

a(n) = A072883(n)^n + n if A072883(n) is not 0, otherwise 0. - Michel Marcus, Mar 27 2020

Corrected and extended by Ray Chandler, Jun 16 2003

One more term from Michel Marcus, Mar 27 2020

A177956 Smallest k > 0 such that k^prime(n) - prime(n) is prime.

Original entry on oeis.org

2, 2, 4, 60, 28, 2, 234, 2, 10, 186, 32, 8, 22, 6, 76, 330, 78, 62, 462, 88, 1416, 1440, 150, 40, 308, 144, 260, 42, 492, 2320, 132, 328, 838, 696, 736, 234, 56, 2786, 172, 382, 4872, 128, 4752, 7292, 826, 1856, 3960, 1124, 424, 612, 2052, 430, 1104, 280, 78, 286

Offset: 1

Ulrich Krug (leuchtfeuer37(AT)gmx.de), May 16 2010

nonn

			1^prime(1)-prime(1) = 1^2-2 = -1 is not prime, but 2^prime(2)-prime(2) = 2^2-2 = 2 is prime, hence a(1) = 2.
k^prime(4)-prime(4) is not prime for k < 60, but 60^prime(4)-prime(4) = 60^7-7 = 2799359999993 is prime, hence a(4) = 60.
a(19)^prime(19)-prime(19) = 462^67-67 has 179 digits.

Cf. A000040, A084046, A084047, A177832.

a177956(n) = {local(k=1, p=prime(n)); while(!isprime(k^p-p), k+=1); k}

Edited, keywords base, hard removed, PARI program and terms a(21) through a(56) added by the Associate Editors of the OEIS Klaus Brockhaus, May 23 2010

Extended by D. S. McNeil, May 23 2010

cp's OEIS Frontend

A084047 Smallest prime p such that p - n is an n-th power, or 0 if no such number exists; i.e., smallest prime of the form k^n + n.

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