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.

Showing 1-4 of 4 results.

A120343 Sequence of pairs numerator(s(n)), denominator(s(n)) where s(n) is the n-th partial sum of 1/A119754(n).

Original entry on oeis.org

1, 5, 16, 55, 327, 935, 382, 935, 9721, 21505, 303414, 623645, 14884103, 29311315, 818168774, 1553499695, 49825457361, 91656482005, 4526122187134, 8157426898445, 1035587163377863, 1851735905947015, 243143544972989094
Offset: 1

Views

Author

Walter Kehowski, Jun 23 2006

Keywords

Comments

There are only 78 terms of A119754 known and s(78) is 0.58817497337288808165551740612048298329310794973566 to 50 decimal places. What is sum(1/A119754(k),k=1..infinity)?

Examples

			a(5)=327, a(6)=935 since s(3)=1/5+1/11+1/17=327/935.

Crossrefs

Cf. A119752, A119754.

Formula

a(2n-1) = numerator(s(n)), a(2n)=denominator(s(n)), where s(n)=sum(1/A119754(k),k=1..n).

Extensions

This is not really a sequence. The standard OEIS convention would be to split this into two cross-referenced sequences with keyword "frac". - N. J. A. Sloane, Jul 22 2006

A120342 Sequence of pairs numerator(s(n)), denominator(s(n)) where s(n) is the n-th partial sum of 1/A119752(n).

Original entry on oeis.org

1, 2, 5, 8, 39, 56, 443, 616, 1783, 2464, 51819, 71456, 4720633, 6502496, 4722257, 6502496, 797359442331, 1097952952096, 878673909876949097, 1209921096197797984, 1351031156635237614515155
Offset: 1

Views

Author

Walter Kehowski, Jun 23 2006

Keywords

Comments

There are only 12 terms of A119752 known and s(12) is 0.72622446726779027806723655668104871423264641644675 to 50 decimal places. What is sum(1/A119752(k),k=1..infinity)?

Examples

			a(5)=39, a(6)=56 since s(3)=1/2+1/8+1/14=39/56.

Crossrefs

Cf. A119752, A119754.

Formula

a(2n-1) = numerator(s(n)), a(2n)=denominator(s(n)), where s(n)=sum(1/A119752(k),k=1..n).

Extensions

This is not really a sequence. The standard OEIS convention would be to split this into two cross-referenced sequences with keyword "frac". - N. J. A. Sloane, Jul 22 2006

A120402 a(1)=2; a(n)=first even number greater than a(n-1) such that 2*a(n)-1 is prime and a(i)+a(n)-1 is prime for all 1<=i<=n-1.

Original entry on oeis.org

2, 4, 10, 70, 430, 4090, 86530, 513100, 913570, 7914340, 6593621380, 9366241600
Offset: 1

Views

Author

Walter Kehowski, Jul 02 2006

Keywords

Comments

All elements after the first are 4 mod 6. In base 12 the sequence is 2, 4, X, 5X, 2EX, 244X, 420XX, 208E24, 38082X, 2798084, where X is 10 and E is eleven.

Examples

			a(2)=4 since 4 is the first even number > a(1)=2 such that 2*4-1=7 is prime and 4+2-1=5 is prime.

Crossrefs

Cf. A119752, A119754, A119751, A119753, A103828.

Programs

  • Maple
    EP:=[2]: for w to 1 do for k from 0 to 12^8 do n:=6*k+4; p:=2*n-1; Q:=map(z-> z+n-1, EP); if isprime(p) and andmap(isprime,Q) then EP:=[op(EP),n]; print(n); fi od od;

Formula

a(1)=2; a(n) = s where s is the first even number s>a(n-1) such that 2*s-1 is prime and s+a(i)-1 is prime, 1<=i<=n-1.

Extensions

a(11)-a(12) from Bert Dobbelaere, Apr 17 2019

A120403 a(1)=3; a(n)=first odd number greater than a(n-1) such that 2*a(n)-1 is prime and a(i)+a(n)-1 is prime for all 1<=i<=n-1.

Original entry on oeis.org

3, 9, 15, 45, 225, 639, 1275, 4005, 675405, 2203959, 3075159, 6195234165, 77989711185, 4566262987329
Offset: 1

Views

Author

Walter Kehowski, Jul 02 2006

Keywords

Comments

All elements are 3 mod 6. In base 12 the sequence is 3, 9, 13, 39, 169, 453, 8X3, 2399, 286X39, 8X3533, 1043733, where X is 10 and E is eleven.

Examples

			a(2)=9 since 9 is the first odd number > a(1)=3 such that 2*9-1=17 is prime and 9+3-1=13 is prime.

Crossrefs

Cf. A119752, A119754 (resulting primes), A119751, A119753, A103828.

Programs

  • Maple
    OP:=[3]: for w to 1 do for k from 0 to 12^8 do n:=6*k+3; p:=2*n-1; Q:=map(z-> z+n-1, OP); if isprime(p) and andmap(isprime,Q) then OP:=[op(OP), n]; print(n); fi od od;

Formula

a(1)=3; a(n) = s where s is the first odd number s>a(n-1) such that 2*s-1 is prime and s+a(i)-1 is prime, 1<=i<=n-1.
a(n) = A119752(n) + 1. - Chandler

Extensions

a(12)-a(14) from Ray Chandler, Apr 04 2010
Showing 1-4 of 4 results.

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