cp's OEIS Frontend

A061344 Numbers of form p^m + 1, p odd prime, m >= 1.

%I A061344 #16 Feb 03 2025 20:08:27
%S A061344 4,6,8,10,12,14,18,20,24,26,28,30,32,38,42,44,48,50,54,60,62,68,72,74,
%T A061344 80,82,84,90,98,102,104,108,110,114,122,126,128,132,138,140,150,152,
%U A061344 158,164,168,170,174,180,182,192,194,198,200,212,224,228,230,234,240
%N A061344 Numbers of form p^m + 1, p odd prime, m >= 1.
%C A061344 Lengths of almost-binary sequences with perfect odd-periodic autocorrelation function.
%C A061344 As J. Arndt points out, each element of this sequence leads to a conference matrix (cf. link to Wikipedia and A000952). - _M. F. Hasler_, Mar 14 2008
%D A061344 H. D. Lueke, Binary odd-periodic complementary sequences. IEEE Trans. Inform. Theory, 43, pp. 365-367, 1997.
%H A061344 M. F. Hasler, <a href="/A061344/b061344.txt">Table of n, a(n) for n = 1..10000</a>
%H A061344 Wikipedia, <a href="http://en.wikipedia.org/wiki/Conference_matrix">Conference matrix</a>.
%o A061344 (PARI) A061344(n)= local(m=1,p); for(c=1,n, until( isprime(m+=2) || ispower(m,[null], && p) && isprime(p),); /*print(c," ",m+1)*/); m+1 \\ - M. F. Hasler, Mar 14 2008
%o A061344 (Python)
%o A061344 from sympy import primepi, integer_nthroot
%o A061344 def A061344(n):
%o A061344     def bisection(f,kmin=0,kmax=1):
%o A061344         while f(kmax) > kmax: kmax <<= 1
%o A061344         kmin = kmax >> 1
%o A061344         while kmax-kmin > 1:
%o A061344             kmid = kmax+kmin>>1
%o A061344             if f(kmid) <= kmid:
%o A061344                 kmax = kmid
%o A061344             else:
%o A061344                 kmin = kmid
%o A061344         return kmax
%o A061344     def f(x): return int(n+x-sum(primepi(integer_nthroot(x,k)[0])-1 for k in range(1,x.bit_length())))
%o A061344     return bisection(f,n+1,n+1)+1 # _Chai Wah Wu_, Feb 03 2025
%Y A061344 Equals A061345 + 1. Cf. A000952.
%K A061344 nonn,easy
%O A061344 1,1
%A A061344 Hans Dieter Lueke (lueke(AT)ient.rwth-aachen.de), Jun 08 2001
%E A061344 More terms from Larry Reeves (larryr(AT)acm.org), Jun 12 2001
%E A061344 Edited by _M. F. Hasler_, Mar 14 2008