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 1-5 of 5 results.

A117459 Indices associated with primes in A117458.

Original entry on oeis.org

49, 65, 269, 304, 344, 379, 469, 517, 553, 557, 647, 658, 683, 928, 1279, 1453, 1457, 1460, 1484, 1499, 1556, 1664, 1682, 1738, 1769, 1796, 1873, 1963, 1967, 2197, 2267, 2290, 2368, 2377, 2485, 2573, 2597, 2609, 2696, 2728, 2791, 2849, 2867, 2975, 2999
Offset: 0

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Author

Enoch Haga, Mar 18 2006

Keywords

Examples

			a(0) = 49 because 49 is the index of the prime 227. When the digits of each are summed, 49 = 4+9 = 13, the next prime after 11 -- formed by summing 2+2+7 = 11 in 227. Since 11 is the prime preceding 13, 49 belongs in the sequence.

Crossrefs

Cf. A117458, A117460-A117463.

Formula

Index SOD's are computed in association with the primes in A117458

A117460 Primes prime(i) such that their sum-of-index-digits A007953(i) and their sum-of-digits A007605(i) are consecutive primes.

Original entry on oeis.org

2, 3, 5, 43, 113, 191, 373, 821, 1097, 1307, 1493, 1523, 1619, 1873, 1907, 2029, 2081, 2339, 3109, 3169, 3347, 3923, 4339, 4421, 4463, 4603, 5417, 5581, 6067, 6263, 6427, 6607, 6791, 6841, 6863, 7127, 7307, 7673, 7723, 7877, 8731, 9341, 10079, 10723
Offset: 1

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Author

Enoch Haga, Mar 18 2006

Keywords

Comments

We select primes such that their sum-of-digits is some prime(j) and such that in addition the sum-of-digits of their index is prime(j-1).
Line 160 of the UBASIC program can be altered for <, >, or = relationships
Subset of A046704 - R. J. Mathar, Apr 17 2009

Examples

			"SOD" = "sum of digits": a(5) = 113, the prime whose index is 30. SOD(30) = 3 and SOD(113) = 5. Since 3 < 5 and 5 is nextprime to 3, adjoin 113 to the sequence.

Crossrefs

Cf. A117461, A117458, A117459, A033548, A033549.

Programs

  • UBASIC
    10 'use of str,mid,len,val 20 'in SOD prime index and SOD prime 30 Y=1 40 Y=nxtprm(Y) 50 C=C+1:print C;Y;"-"; 60 D=str(C):Z=str(Y) 70 E=len(D):F=len(Z) 80 for Q=2 to E 90 A=mid(D,Q,1):G=val(A) 100 I=I+G:print I; 110 next Q 120 for R=2 to F 130 B=mid(Z,R,1):H=val(B) 140 J=J+H:print J; 150 next R 160 if I=prmdiv(I) and J=prmdiv(J) and I>J and I=nxtprm(J) then stop 170 I=0:J=0 180 goto 40

Formula

{A000040(i): A007605(i) = A000040(j) and A007953(i) = A000040(j+1) for some j}. - R. J. Mathar, Apr 17 2009

Extensions

Edited by R. J. Mathar, Apr 17 2009

A117461 Indices associated with primes in A117460. Both primes and their indices, after calculation of their respective digit sums, bear the relationship that both are prime and that sod(i) < sod(p) and sod(p) is the next prime after to sod(i), where sod is the sum of digits function.

Original entry on oeis.org

1, 2, 3, 14, 30, 43, 74, 142, 184, 214, 238, 241, 256, 287, 292, 308, 313, 346, 443, 449, 472, 544, 593, 601, 607, 623, 715, 737, 791, 814, 836, 854, 874, 881, 883, 913, 931, 973, 980, 995, 1088, 1156, 1237, 1307, 1316, 1343, 1381, 1396, 1462, 1565, 1622
Offset: 0

Views

Author

Enoch Haga, Mar 18 2006

Keywords

Comments

A117458-A117459 is the opposite case where sod(i) > sod(p).
A117460-A117461 is sod(i) < sod(p).
A033548-A033549 is sod(i) = sod(p). - G. L. Honaker, Jr.

Examples

			a(4) = 30. Its associated prime is 113 with sod = 5; sod(a(4)) = 3. Since 3 < 5 and 5 is the next prime after 3, a(4) belongs in the sequence.

Crossrefs

Cf. A007953 (sum of digits).
Cf. A117460, A117458, A117459, A033548, A033549.

Programs

  • UBASIC
    10 'use of str,mid,len,val
20 'in SOD prime index and SOD prime
30 Y=1
40 Y=nxtprm(Y)
50 C=C+1:print C;Y;"-";
60 D=str(C):Z=str(Y)
70 E=len(D):F=len(Z)
80 for Q=2 to E
90 A=mid(D,Q,1):G=val(A)
100 I=I+G:print I;
110 next Q
120 for R=2 to F
130 B=mid(Z,R,1):H=val(B)
140 J=J+H:print J;
150 next R
160 if I=prmdiv(I) and J=prmdiv(J) and I

Formula

SOD's are calculated for these indices; if they and their associated prime SOD's are both prime and bear the relation in the Brief description above, they are added to the sequence.

A117477 Primes whose SOD and that of their indices are both prime and equal (indices may not be prime, but their SOD must be prime).

Original entry on oeis.org

131, 263, 1039, 1091, 1301, 1361, 1433, 2221, 2441, 2591, 2663, 2719, 2803, 3433, 3631, 4153, 4357, 4397, 5507, 5701, 5741, 5927, 6311, 6353, 6553, 6737, 6827, 6971, 7013, 7213, 7411, 7523, 7741, 8821, 9103, 11173, 11353, 11731, 11821, 12277, 12347
Offset: 1

Views

Author

Enoch Haga, Mar 19 2006

Keywords

Comments

"SOD" = "sum of digits".
This sequence is a subset of A033548, the difference being that this sequence requires prime SODs.

Examples

			a(3) = 1039, the 175th prime. Both the SOD of the index and the prime are prime and equal: 13 = 13.

Links

Crossrefs

Cf. A117478, A033548-A033549, A117458-A117463.

Programs

  • Mathematica
    sodQ[{n_,p_}]:=Module[{sodn=Total[IntegerDigits[n]],sodp=Total[IntegerDigits[p]]},AllTrue[ {sodn,sodp},PrimeQ] && sodn == sodp]; Select[With[{nn=1500},Table[{n,Prime[n]},{n,nn}]],sodQ][[;;,2]] (* Harvey P. Dale, Apr 20 2024 *)
  • UBASIC
    20 'SOD prime index and SOD prime
30 Y=1
40 Y=nxtprm(Y)
50 C=C+1:print C;Y;"-";
60 D=str(C):Z=str(Y)
70 E=len(D):F=len(Z)
80 for Q=2 to E
90 A=mid(D,Q,1):G=val(A)
100 I=I+G:print I;
110 next Q
120 for R=2 to F
130 B=mid(Z,R,1):H=val(B)
140 J=J+H:print J;
150 next R
160 if I=prmdiv(I) and J=prmdiv(J) and I=J then stop
170 I=0:J=0
180 goto 40

Formula

Find primes whose indices, when SODs are computed, are both prime and SOD(i) = SOD(p)

A117478 Indices of associated primes in A117477.

Original entry on oeis.org

32, 56, 175, 182, 212, 218, 227, 331, 362, 377, 386, 397, 409, 481, 508, 571, 595, 599, 728, 751, 755, 779, 821, 827, 847, 869, 878, 896, 902, 922, 940, 953, 982, 1099, 1129, 1354, 1372, 1408, 1417, 1468, 1475, 1507, 1550, 1585, 1648, 1693, 1747, 1772, 1774
Offset: 0

Views

Author

Enoch Haga, Mar 19 2006

Keywords

Comments

A subset of A033548-A033549 but here the SODs must be prime and equal

Examples

			a(3) = 182, with SOD 11. The associated prime is 1091, also SOD 11. SODs must be prime and equal.

Crossrefs

Cf. A117477, A033548-A033549, A117458-A117463.

Programs

  • UBASIC
    20 'SOD prime index and SOD prime
30 Y=1
40 Y=nxtprm(Y)
50 C=C+1:print C;Y;"-";
60 D=str(C):Z=str(Y)
70 E=len(D):F=len(Z)
80 for Q=2 to E
90 A=mid(D,Q,1):G=val(A)
100 I=I+G:print I;
110 next Q
120 for R=2 to F
130 B=mid(Z,R,1):H=val(B)
140 J=J+H:print J;
150 next R
160 if I=prmdiv(I) and J=prmdiv(J) and I=J then stop
170 I=0:J=0
180 goto 40

Formula

Find prime indices with associated primes where both SODs are the same and prime.

Extensions

Typo in comment fixed by Franklin T. Adams-Watters, Dec 03 2009
Showing 1-5 of 5 results.

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