A253906 -id:A253906 - cp's OEIS frontend

A253907 Numbers n such that n^2 + 3, n^3 + 3, n^4 + 3, n^5 + 3, n^6 + 3 and n^7 + 3 are semiprime.

1, 976, 5380, 16582, 17864, 22316, 27922, 34930, 44954, 50744, 61264, 72670, 107534, 147776, 193774, 195266, 240170, 260920, 265292, 281582, 314462, 337832, 342014, 367060, 379784, 383930, 384704, 392050, 421226, 455734, 463790, 498134, 499306, 510194, 538384

Offset: 1

K. D. Bajpai, Jan 24 2015

nonn

All terms in this sequence, except a(1), are even.

Subsequence of A253906.

			a(2) = 976;
976^2 + 3 = 952579 = 43 * 22153;
976^3 + 3 = 929714179 = 1013 * 917783;
976^4 + 3 = 907401035779 = 7 * 129628719397;
976^5 + 3 = 885623410917379 = 2224441 * 398133019;
976^6 + 3 = 864368449055358979 = 97327 * 8881075642477;
976^7 + 3 = 843623606278030360579 = 16403765263 * 51428656333;
All six are semiprime.

K. D. Bajpai, Table of n, a(n) for n = 1..555

Cf. A001358, A108868, A242331, A253906.

Select[Range[10^5], k = 3; PrimeOmega[(#^2 + k)] == 2 && PrimeOmega[(#^3 + k)] == 2 && PrimeOmega[(#^4 + k)] == 2 && PrimeOmega[(#^5 + k)] == 2 &&  PrimeOmega[(#^6 + k)] == 2  && PrimeOmega[(#^7 + k)] == 2 &]
Select[Range[54*10^4],Union[PrimeOmega[#^Range[2,7]+3]]=={2}&] (* Harvey P. Dale, Jul 30 2022 *)

A059582 First differences give digits of Pi = 3.1415926...

Original entry on oeis.org

1, 4, 5, 9, 10, 15, 24, 26, 32, 37, 40, 45, 53, 62, 69, 78, 81, 83, 86, 94, 98, 104, 106, 112, 116, 119, 122, 130, 133, 135, 142, 151, 156, 156, 158, 166, 174, 178, 179, 188, 195, 196, 202, 211, 214, 223, 232, 235, 242, 247, 248, 248, 253, 261, 263, 263, 272

Offset: 0

Rodolfo Kurchan, Feb 17 2001

A more natural variant is given by A046974, the partial sums of the digits of Pi (A000796). Maybe the present version is motivated by the coincidence that the first four digits 1,4,5,9 are similar to the decimals .14159 of Pi. - M. F. Hasler, Jan 19 2015

Harry J. Smith, Table of n, a(n) for n = 0..2000
A. Frank & P. Jacqueroux, International Contest, 2001. Item 14

Cf. A253906, A253907.

Digits := 200: it := evalf(Pi, 200)/10: out := 1: for i from 1 to 200 do printf(`%d,`,out): out := out+floor(10*it): it := 10*it-floor(10*it): od:

Accumulate[Join[{1},RealDigits[Pi,10,60][[1]]]] (* Harvey P. Dale, Jan 18 2015 *)

{ default(realprecision, 2080); a=1; x=Pi/10; for (n=0, 2000, d=floor(x); x=(x-d)*10; write("b059582.txt", n, " ", a+=d)); } \\ Harry J. Smith, Jun 28 2009

More terms from James Sellers, Feb 19 2001

cp's OEIS Frontend

A253907 Numbers n such that n^2 + 3, n^3 + 3, n^4 + 3, n^5 + 3, n^6 + 3 and n^7 + 3 are semiprime.

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