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.

User: Tomas Xordan

Tomas Xordan's wiki page.

Tomas Xordan has authored 43 sequences. Here are the ten most recent ones:

A129079 Prime numbers that are the sum of consecutive prime numbers with the final digit 7 (primes in A030432).

Original entry on oeis.org

7, 61, 379, 643, 967, 2549, 9547, 19531, 45121, 70199, 78467, 127637, 150373, 156257, 175069, 195311, 209459, 246709, 286999, 295513, 312931, 330859, 349207, 378239, 398357, 518191, 553733, 765287, 779731, 838927, 853981, 1166597
Offset: 1

Views

Author

Tomas Xordan, May 11 2007

Keywords

Examples

			a(6)=2549 because 2549=A030432(1)+ A030432(2)+A030432(3)+A030432(4)+ A030431(5)+A030432(6)+A030432(7)+ A030432(8)+A030432(9)+A030432(10)+A030432(11)+A030432(12)+A030432(13)+A030432(14)+A030432(15)+A030432(16)+A030432(17)= 7+ 17+ 37+ 47+ 67+ 97+ 107+ 127+ 137+ 157+ 167+ 197+ 227+ 257+ 277+ 307+ 317; and 2549 is a prime number.

Crossrefs

Cf. A030432; A000040.

Formula

a(n)=A030432(1)+A030432(2)+...+A030432(x); a is a prime number.

A129537 Prime numbers p of the form p=x^2+y^3 such that there exist three other prime numbers q,r,s such q=abs(x^2-y^3) ; r=x^3+y^2 ; s=abs(x^3-y^2); x > y.

Original entry on oeis.org

127, 449, 811, 2089, 2521, 4651, 4969, 6427, 13697, 17351, 23831, 38393, 52321, 53569, 69119, 69767, 112571, 113021, 116089, 143257, 156941, 168409, 171757, 196561, 197569, 228751, 250489, 250969, 294641, 328121, 337627, 350281, 355321
Offset: 1

Views

Author

Tomas Xordan, May 29 2007

Keywords

Examples

			p=a(1)= 127 because:
P=127=10^2+3^3=100+27;
q=73=10^2-3^3=100-27;
r=1009=10^3+3^2=1000+9;
s=991=10^3-3^2=1000-9

Crossrefs

Cf. A000040.

Formula

a(n)=p=x^2+y^3; q=x^2-y3;r=x^3+y^2;s=x^3-y^2 ; x > y ; a(n),q,r,s are prime numbers.

A130006 Prime numbers arising from A050704.

Original entry on oeis.org

2, 3, 3, 5, 5, 7, 11, 11, 11, 17, 19, 23, 17, 23, 29, 29, 37, 31, 43, 43, 29, 47, 47, 43, 53, 59, 67, 41, 71, 71, 59, 71, 83, 71, 97, 83, 59, 79, 89, 83, 107, 113, 71, 107, 127, 103, 131, 157, 137, 173, 179, 131, 167, 101, 179, 193, 139, 167, 179, 107, 191, 197, 173
Offset: 1

Views

Author

Tomas Xordan, Jun 15 2007

Keywords

Examples

			a(10)=17 because A050704(10) - prime factors of A050704(10) = 28-(7+2+2)=28-11=17.

Crossrefs

Cf. A050704.

Formula

a(n)=A050704(n) - (prime factors of A050704(n)).

A130468 Primes q of the form a^3+b^2, such that p =A130467(n)= a^2+b^3 is prime and smaller than q; p < q ; b < a.

Original entry on oeis.org

31, 73, 733, 359, 1009, 2753, 2213, 1753, 1367, 1049, 5857, 1777, 21961, 13873, 8081, 10729, 6959, 54881, 36037, 91141, 59419, 110641, 140617, 43019, 3571, 157489, 157513, 195121, 140689, 195193, 274661, 314441, 15881, 227081, 250147, 6121
Offset: 1

Views

Author

Tomas Xordan, May 27 2007

Keywords

Examples

			a(5)=1009 because 1009=10^3+3^2 and A130467(5)=127 =10^2 + 3^3 ; 127 >1009; 3 > 10

Crossrefs

Cf. A130467; A000040.

Formula

q=a^2+b^3; p=a^3+b^2; p < q ; a < b

A130474 Prime numbers p of the form p=x^2+y^3 such that q =A130475(n)= abs(x^2-y^3) is prime and smaller than p.

Original entry on oeis.org

5, 31, 43, 89, 127, 241, 269, 283, 379, 449, 449, 487, 521, 593, 811, 919, 953, 1009, 1051, 1601, 2017, 2089, 2089, 2143, 2341, 2521, 2521, 2609, 2731, 2953, 3041, 3163, 3391, 3631, 3943, 4051, 4129, 4159, 4481, 4481, 4651, 4931, 4969, 5113, 5209, 5309
Offset: 1

Views

Author

Tomas Xordan, May 28 2007

Keywords

Examples

			a(4)= 89 because 89= 9^2+2^3= 81 + 8 and A130475(4)= 73 =abs(9^2-2^3)= abs(81-8) ; A130475(4) < a(4) ; A130475(4) and a(4) are prime numbers, members of A000040.
a(5)= 127 because 127= 10^2+ 3^3= 100 + 27 and A130475(5)= 73 = abs(10^2-3^3)= abs(100-27) ; A130475(5) < a(5) ; A130475(5) and a(5) are prime numbers, members of A000040.
a(9)= 379 because 379= 6^2 + 7^3= 36 + 343 and A130475(9)= 307 = abs(6^2-7^3)= abs(36-343) ; A130475(9) < a(9) ; A130475(9) and a(9) are prime numbers, members of A000040.

Crossrefs

Cf. A000040; A130475.

Formula

a(n)= x^2+y^3 and A130475(n)=q=abs(x^2-y^3); a(n) > A130475(n);a(n) and A130475(n) are in A000040 (prime numbers)

A130475 Prime numbers q of the form q=abs(x^2-y^3) such that p =A130474(n)= x^2+y^3 is prime and greater than q. (Prime numbers arising from A130474).

Original entry on oeis.org

3, 23, 11, 73, 73, 191, 19, 229, 307, 199, 433, 199, 503, 431, 757, 233, 71, 991, 997, 577, 1439, 1367, 89, 2089, 2053, 1873, 521, 2593, 2677, 503, 2791, 3109, 3359, 3119, 3257, 2699, 673, 2591, 3457, 4231, 4597, 2269, 2969, 719, 1753, 5059, 1993, 5449
Offset: 1

Views

Author

Tomas Xordan, May 28 2007

Keywords

Examples

			a(4)= 73 because 73= abs(9^2-2^3)= abs(81 - 8 ) and A130474(4)= 89 =9^2+2^3= 81+8 ; A130474(4) > a(4) ; A130474(4) and a(4) are prime numbers, members of A000040.
a(5)= 73 because 73=abs(10^2-3^3)= abs(100 - 27) and A130474(5)= 127 = 10^2+3^3= 100+27 ; A130474(5) > a(5) ; A130474(5) and a(5) are prime numbers, members of A000040.
a(9)= 307 because 307= abs(6^2 - 7^3)=abs(36 - 343) and A130474(9)= 379 = 6^2+7^3= 36+343 ; A130474(9) > a(9) ; A130474(9) and a(9) are prime numbers, members of A000040.

Crossrefs

Cf. A000040; A130474.

Formula

a(n)= abs(x^2-y^3) and A130474(n)=p=x^2+y^3; a(n) < A130474(n); a(n) and A130474(n) are in A000040 (prime numbers)

A131102 Prime numbers arising from A131101.

Original entry on oeis.org

2, 5, 7, 11, 23, 47, 37, 59, 41, 43, 47, 83, 107, 73, 83, 89, 97, 167, 179, 227, 139, 137, 151, 263, 151, 167, 157, 197, 347, 193, 359, 223, 383, 229, 241, 467, 479, 257, 293, 503, 281, 307, 283, 307, 317, 563, 313, 313, 587, 331, 349, 349, 367, 367, 419, 719
Offset: 1

Views

Author

Tomas Xordan, Jun 14 2007

Keywords

Comments

The Safe Primes (A005385) are part of this sequence because they are the result of adding A005384(n) (Sophie Germain primes) to its only prime factor (itself) + 1 = 2*A005384 + 1 .

Examples

			a(8)=59 because 59 = A131101(8)+ prime factors of A131101(8) +1 = 29+ (29) +1.
a(9)=41 because A131101(9)+ prime factors of A131101(8) + 1 = 30 +(2+3+5)+1.

Crossrefs

Cf. A131101, A005384, A005385.

Formula

A131101(n) + prime factors of A131101(n) + 1 = a(n) ; a(n) is a prime number.

A129078 Prime numbers that are the sum of consecutive prime numbers with the final digit 3 (primes in A030431).

Original entry on oeis.org

3, 1259, 51241, 81749, 230149, 245621, 253567, 269879, 286801, 331301, 482731, 540041, 551917, 564013, 625943, 638669, 746777, 975427, 1093129, 1145537, 1181149, 1272679, 1528187, 1569479, 1675679, 1741517, 1970867, 2066951
Offset: 1

Views

Author

Tomas Xordan, May 11 2007

Keywords

Examples

			a(2)=1259 because 1259=A030431(1)+ A030431(2)+A030431(3)+A030431(4)+ A030431(5)+A030431(6)+A030431(7)+ A030431(8)+A030431(9)+A030431(10)+A030431(11)+A030431(12)+A030431(13)= 3+ 13+ 23+ 43+ 53+ 73+ 83+ 103+ 113+ 163+ 173+ 193+ 223 and 1259 is a prime number.

Crossrefs

Cf. A030431; A000040.

Programs

  • Mathematica
    Select[Accumulate[Select[10Range[0,1500]+3,PrimeQ]],PrimeQ]  (* Harvey P. Dale, Apr 06 2011 *)

Formula

a(n)=A030431(1)+A030431(2)+...+A030431(x); a is a prime number.

A129748 Numbers n such that the sum of the first n primes with the final digit 9 is prime.

Original entry on oeis.org

1, 3, 7, 11, 13, 19, 37, 39, 61, 73, 89, 107, 109, 113, 117, 147, 153, 159, 171, 173, 207, 241, 253, 307, 311, 329, 347, 419, 429, 461, 481, 491, 497, 509, 523, 529, 539, 543, 559, 613, 617, 631, 651, 691, 701, 703, 731, 737, 741, 753, 799, 809, 813, 823, 827
Offset: 1

Views

Author

Tomas Xordan, May 14 2007

Keywords

Crossrefs

Cf. A129081; A000040; A030433.

Programs

Formula

a(n)=primes in A030433 added to obtain A129081(n)

A129081 Primes appearing in partial sums of A030433 (primes ending in 9).

Original entry on oeis.org

19, 107, 523, 1279, 1787, 4091, 16103, 18041, 46889, 68437, 104561, 155443, 161641, 174367, 187573, 303473, 330587, 359231, 419929, 430517, 634793, 878939, 974507, 1469753, 1510319, 1700851, 1902653, 2836961, 2982841, 3476299, 3807589
Offset: 1

Views

Author

Tomas Xordan, May 11 2007

Keywords

Examples

			a(5) = 1787 because 1787 = A030433(1) + A030433(2) + A030433(3) + A030433(4) + A030433(5) + A030433(6) + A030433(7) + A030433(8) + A030433(9) + A030433(10) + A030433(11) + A030433(12) + A030433(13) = 19 + 29 + 59 + 79 + 89 + 109 + 139 + 149 + 179 + 199 + 229 + 239 + 269; and 1787 is a prime number.

Links

Crossrefs

Cf. A030433, A000040.

Programs

  • GAP
    P:=Filtered(List([1..5*10^5],n->10*n+9),IsPrime);;
a:=Filtered(List([1..Length(P)],i->Sum([1..i],k->P[k])),IsPrime); # Muniru A Asiru, Apr 28 2018
  • Mathematica
    With[{pr9s=Select[Prime[Range[3000]],Last[IntegerDigits[#]]==9&]}, Select[ Accumulate[ pr9s],PrimeQ]] (* Harvey P. Dale, Dec 31 2011 *)
  • PARI
    {s=0; forprime(p=2, 17300, if(p%10==9, s+=p; if(isprime(s), print1(s, ","))))} /* Klaus Brockhaus, May 13 2007 */

Formula

a(n) = A030433(1)+A030433(2)+...+A030433(x); a is a prime number.

Extensions

Entries checked by Klaus Brockhaus, May 13 2007
Better description from Harvey P. Dale, Dec 31 2011

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